Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models.

PubMed

Haem, Elham; Harling, Kajsa; Ayatollahi, Seyyed Mohammad Taghi; Zare, Najaf; Karlsson, Mats O

2017-02-01

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

Goodness-Of-Fit Test for Nonparametric Regression Models: Smoothing Spline ANOVA Models as Example.

PubMed

Teran Hidalgo, Sebastian J; Wu, Michael C; Engel, Stephanie M; Kosorok, Michael R

2018-06-01

Nonparametric regression models do not require the specification of the functional form between the outcome and the covariates. Despite their popularity, the amount of diagnostic statistics, in comparison to their parametric counter-parts, is small. We propose a goodness-of-fit test for nonparametric regression models with linear smoother form. In particular, we apply this testing framework to smoothing spline ANOVA models. The test can consider two sources of lack-of-fit: whether covariates that are not currently in the model need to be included, and whether the current model fits the data well. The proposed method derives estimated residuals from the model. Then, statistical dependence is assessed between the estimated residuals and the covariates using the HSIC. If dependence exists, the model does not capture all the variability in the outcome associated with the covariates, otherwise the model fits the data well. The bootstrap is used to obtain p-values. Application of the method is demonstrated with a neonatal mental development data analysis. We demonstrate correct type I error as well as power performance through simulations.

Use and Impact of Covariance Data in the Japanese Latest Adjusted Library ADJ2010 Based on JENDL-4.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yokoyama, K., E-mail: yokoyama.kenji09@jaea.go.jp; Ishikawa, M.

2015-01-15

The current status of covariance applications to fast reactor analysis and design in Japan is summarized. In Japan, the covariance data are mainly used for three purposes: (1) to quantify the uncertainty of nuclear core parameters, (2) to identify important nuclides, reactions and energy ranges which are dominant to the uncertainty of core parameters, and (3) to improve the accuracy of core design values by adopting the integral data such as the critical experiments and the power reactor operation data. For the last purpose, the cross section adjustment based on the Bayesian theorem is used. After the release of JENDL-4.0,more » a development project of the new adjusted group-constant set ADJ2010 was started in 2010 and completed in 2013. In the present paper, the final results of ADJ2010 are briefly summarized. In addition, the adjustment results of ADJ2010 are discussed from the viewpoint of use and impact of nuclear data covariances, focusing on {sup 239}Pu capture cross section alterations. For this purpose three kind of indices, called “degree of mobility,” “adjustment motive force,” and “adjustment potential,” are proposed.« less

A Simulation Study on the Performance of the Simple Difference and Covariance-Adjusted Scores in Randomized Experimental Designs.

PubMed

Petscher, Yaacov; Schatschneider, Christopher

2011-01-01

Research by Huck and McLean (1975) demonstrated that the covariance-adjusted score is more powerful than the simple difference score, yet recent reviews indicate researchers are equally likely to use either score type in two-wave randomized experimental designs. A Monte Carlo simulation was conducted to examine the conditions under which the simple difference and covariance-adjusted scores were more or less powerful to detect treatment effects when relaxing certain assumptions made by Huck and McLean (1975). Four factors were manipulated in the design including sample size, normality of the pretest and posttest distributions, the correlation between pretest and posttest, and posttest variance. A 5 × 5 × 4 × 3 mostly crossed design was run with 1,000 replications per condition, resulting in 226,000 unique samples. The gain score was nearly as powerful as the covariance-adjusted score when pretest and posttest variances were equal, and as powerful in fan-spread growth conditions; thus, under certain circumstances the gain score could be used in two-wave randomized experimental designs.

A Simulation Study on the Performance of the Simple Difference and Covariance-Adjusted Scores in Randomized Experimental Designs

PubMed Central

Petscher, Yaacov; Schatschneider, Christopher

2015-01-01

Research by Huck and McLean (1975) demonstrated that the covariance-adjusted score is more powerful than the simple difference score, yet recent reviews indicate researchers are equally likely to use either score type in two-wave randomized experimental designs. A Monte Carlo simulation was conducted to examine the conditions under which the simple difference and covariance-adjusted scores were more or less powerful to detect treatment effects when relaxing certain assumptions made by Huck and McLean (1975). Four factors were manipulated in the design including sample size, normality of the pretest and posttest distributions, the correlation between pretest and posttest, and posttest variance. A 5 × 5 × 4 × 3 mostly crossed design was run with 1,000 replications per condition, resulting in 226,000 unique samples. The gain score was nearly as powerful as the covariance-adjusted score when pretest and posttest variances were equal, and as powerful in fan-spread growth conditions; thus, under certain circumstances the gain score could be used in two-wave randomized experimental designs. PMID:26379310

Mental Health Risk Adjustment with Clinical Categories and Machine Learning.

PubMed

Shrestha, Akritee; Bergquist, Savannah; Montz, Ellen; Rose, Sherri

2017-12-15

To propose nonparametric ensemble machine learning for mental health and substance use disorders (MHSUD) spending risk adjustment formulas, including considering Clinical Classification Software (CCS) categories as diagnostic covariates over the commonly used Hierarchical Condition Category (HCC) system. 2012-2013 Truven MarketScan database. We implement 21 algorithms to predict MHSUD spending, as well as a weighted combination of these algorithms called super learning. The algorithm collection included seven unique algorithms that were supplied with three differing sets of MHSUD-related predictors alongside demographic covariates: HCC, CCS, and HCC + CCS diagnostic variables. Performance was evaluated based on cross-validated R 2 and predictive ratios. Results show that super learning had the best performance based on both metrics. The top single algorithm was random forests, which improved on ordinary least squares regression by 10 percent with respect to relative efficiency. CCS categories-based formulas were generally more predictive of MHSUD spending compared to HCC-based formulas. Literature supports the potential benefit of implementing a separate MHSUD spending risk adjustment formula. Our results suggest there is an incentive to explore machine learning for MHSUD-specific risk adjustment, as well as considering CCS categories over HCCs. © Health Research and Educational Trust.

On the Importance of Reliable Covariate Measurement in Selection Bias Adjustments Using Propensity Scores

ERIC Educational Resources Information Center

Steiner, Peter M.; Cook, Thomas D.; Shadish, William R.

2011-01-01

The effect of unreliability of measurement on propensity score (PS) adjusted treatment effects has not been previously studied. The authors report on a study simulating different degrees of unreliability in the multiple covariates that were used to estimate the PS. The simulation uses the same data as two prior studies. Shadish, Clark, and Steiner…

Estimation of group means when adjusting for covariates in generalized linear models.

PubMed

Qu, Yongming; Luo, Junxiang

2015-01-01

Generalized linear models are commonly used to analyze categorical data such as binary, count, and ordinal outcomes. Adjusting for important prognostic factors or baseline covariates in generalized linear models may improve the estimation efficiency. The model-based mean for a treatment group produced by most software packages estimates the response at the mean covariate, not the mean response for this treatment group for the studied population. Although this is not an issue for linear models, the model-based group mean estimates in generalized linear models could be seriously biased for the true group means. We propose a new method to estimate the group mean consistently with the corresponding variance estimation. Simulation showed the proposed method produces an unbiased estimator for the group means and provided the correct coverage probability. The proposed method was applied to analyze hypoglycemia data from clinical trials in diabetes. Copyright © 2014 John Wiley & Sons, Ltd.

Sensitivity analysis for missing dichotomous outcome data in multi-visit randomized clinical trial with randomization-based covariance adjustment.

PubMed

Li, Siying; Koch, Gary G; Preisser, John S; Lam, Diana; Sanchez-Kam, Matilde

2017-01-01

Dichotomous endpoints in clinical trials have only two possible outcomes, either directly or via categorization of an ordinal or continuous observation. It is common to have missing data for one or more visits during a multi-visit study. This paper presents a closed form method for sensitivity analysis of a randomized multi-visit clinical trial that possibly has missing not at random (MNAR) dichotomous data. Counts of missing data are redistributed to the favorable and unfavorable outcomes mathematically to address possibly informative missing data. Adjusted proportion estimates and their closed form covariance matrix estimates are provided. Treatment comparisons over time are addressed with Mantel-Haenszel adjustment for a stratification factor and/or randomization-based adjustment for baseline covariables. The application of such sensitivity analyses is illustrated with an example. An appendix outlines an extension of the methodology to ordinal endpoints.

Variable Selection for Nonparametric Quantile Regression via Smoothing Spline AN OVA

PubMed Central

Lin, Chen-Yen; Bondell, Howard; Zhang, Hao Helen; Zou, Hui

2014-01-01

Quantile regression provides a more thorough view of the effect of covariates on a response. Nonparametric quantile regression has become a viable alternative to avoid restrictive parametric assumption. The problem of variable selection for quantile regression is challenging, since important variables can influence various quantiles in different ways. We tackle the problem via regularization in the context of smoothing spline ANOVA models. The proposed sparse nonparametric quantile regression (SNQR) can identify important variables and provide flexible estimates for quantiles. Our numerical study suggests the promising performance of the new procedure in variable selection and function estimation. Supplementary materials for this article are available online. PMID:24554792

Nonparametric Bayesian models for a spatial covariance.

PubMed

Reich, Brian J; Fuentes, Montserrat

2012-01-01

A crucial step in the analysis of spatial data is to estimate the spatial correlation function that determines the relationship between a spatial process at two locations. The standard approach to selecting the appropriate correlation function is to use prior knowledge or exploratory analysis, such as a variogram analysis, to select the correct parametric correlation function. Rather that selecting a particular parametric correlation function, we treat the covariance function as an unknown function to be estimated from the data. We propose a flexible prior for the correlation function to provide robustness to the choice of correlation function. We specify the prior for the correlation function using spectral methods and the Dirichlet process prior, which is a common prior for an unknown distribution function. Our model does not require Gaussian data or spatial locations on a regular grid. The approach is demonstrated using a simulation study as well as an analysis of California air pollution data.

Directional variance adjustment: bias reduction in covariance matrices based on factor analysis with an application to portfolio optimization.

PubMed

Bartz, Daniel; Hatrick, Kerr; Hesse, Christian W; Müller, Klaus-Robert; Lemm, Steven

2013-01-01

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.

INVESTIGATING DIFFERENCES IN BRAIN FUNCTIONAL NETWORKS USING HIERARCHICAL COVARIATE-ADJUSTED INDEPENDENT COMPONENT ANALYSIS.

PubMed

Shi, Ran; Guo, Ying

2016-12-01

Human brains perform tasks via complex functional networks consisting of separated brain regions. A popular approach to characterize brain functional networks in fMRI studies is independent component analysis (ICA), which is a powerful method to reconstruct latent source signals from their linear mixtures. In many fMRI studies, an important goal is to investigate how brain functional networks change according to specific clinical and demographic variabilities. Existing ICA methods, however, cannot directly incorporate covariate effects in ICA decomposition. Heuristic post-ICA analysis to address this need can be inaccurate and inefficient. In this paper, we propose a hierarchical covariate-adjusted ICA (hc-ICA) model that provides a formal statistical framework for estimating covariate effects and testing differences between brain functional networks. Our method provides a more reliable and powerful statistical tool for evaluating group differences in brain functional networks while appropriately controlling for potential confounding factors. We present an analytically tractable EM algorithm to obtain maximum likelihood estimates of our model. We also develop a subspace-based approximate EM that runs significantly faster while retaining high accuracy. To test the differences in functional networks, we introduce a voxel-wise approximate inference procedure which eliminates the need of computationally expensive covariance matrix estimation and inversion. We demonstrate the advantages of our methods over the existing method via simulation studies. We apply our method to an fMRI study to investigate differences in brain functional networks associated with post-traumatic stress disorder (PTSD).

Directional Variance Adjustment: Bias Reduction in Covariance Matrices Based on Factor Analysis with an Application to Portfolio Optimization

PubMed Central

Bartz, Daniel; Hatrick, Kerr; Hesse, Christian W.; Müller, Klaus-Robert; Lemm, Steven

2013-01-01

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation. PMID:23844016

Marginally specified priors for non-parametric Bayesian estimation

PubMed Central

Kessler, David C.; Hoff, Peter D.; Dunson, David B.

2014-01-01

Summary Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables. PMID:25663813

A complete graphical criterion for the adjustment formula in mediation analysis.

PubMed

Shpitser, Ilya; VanderWeele, Tyler J

2011-03-04

Various assumptions have been used in the literature to identify natural direct and indirect effects in mediation analysis. These effects are of interest because they allow for effect decomposition of a total effect into a direct and indirect effect even in the presence of interactions or non-linear models. In this paper, we consider the relation and interpretation of various identification assumptions in terms of causal diagrams interpreted as a set of non-parametric structural equations. We show that for such causal diagrams, two sets of assumptions for identification that have been described in the literature are in fact equivalent in the sense that if either set of assumptions holds for all models inducing a particular causal diagram, then the other set of assumptions will also hold for all models inducing that diagram. We moreover build on prior work concerning a complete graphical identification criterion for covariate adjustment for total effects to provide a complete graphical criterion for using covariate adjustment to identify natural direct and indirect effects. Finally, we show that this criterion is equivalent to the two sets of independence assumptions used previously for mediation analysis.

The Covariance Adjustment Approaches for Combining Incomparable Cox Regressions Caused by Unbalanced Covariates Adjustment: A Multivariate Meta-Analysis Study.

PubMed

Dehesh, Tania; Zare, Najaf; Ayatollahi, Seyyed Mohammad Taghi

2015-01-01

Univariate meta-analysis (UM) procedure, as a technique that provides a single overall result, has become increasingly popular. Neglecting the existence of other concomitant covariates in the models leads to loss of treatment efficiency. Our aim was proposing four new approximation approaches for the covariance matrix of the coefficients, which is not readily available for the multivariate generalized least square (MGLS) method as a multivariate meta-analysis approach. We evaluated the efficiency of four new approaches including zero correlation (ZC), common correlation (CC), estimated correlation (EC), and multivariate multilevel correlation (MMC) on the estimation bias, mean square error (MSE), and 95% probability coverage of the confidence interval (CI) in the synthesis of Cox proportional hazard models coefficients in a simulation study. Comparing the results of the simulation study on the MSE, bias, and CI of the estimated coefficients indicated that MMC approach was the most accurate procedure compared to EC, CC, and ZC procedures. The precision ranking of the four approaches according to all above settings was MMC ≥ EC ≥ CC ≥ ZC. This study highlights advantages of MGLS meta-analysis on UM approach. The results suggested the use of MMC procedure to overcome the lack of information for having a complete covariance matrix of the coefficients.

Modeling SF-6D Hong Kong standard gamble health state preference data using a nonparametric Bayesian method.

PubMed

Kharroubi, Samer A; Brazier, John E; McGhee, Sarah

2013-01-01

This article reports on the findings from applying a recently described approach to modeling health state valuation data and the impact of the respondent characteristics on health state valuations. The approach applies a nonparametric model to estimate a Bayesian six-dimensional health state short form (derived from short-form 36 health survey) health state valuation algorithm. A sample of 197 states defined by the six-dimensional health state short form (derived from short-form 36 health survey)has been valued by a representative sample of the Hong Kong general population by using standard gamble. The article reports the application of the nonparametric model and compares it to the original model estimated by using a conventional parametric random effects model. The two models are compared theoretically and in terms of empirical performance. Advantages of the nonparametric model are that it can be used to predict scores in populations with different distributions of characteristics than observed in the survey sample and that it allows for the impact of respondent characteristics to vary by health state (while ensuring that full health passes through unity). The results suggest an important age effect with sex, having some effect, but the remaining covariates having no discernible effect. The nonparametric Bayesian model is argued to be more theoretically appropriate than previously used parametric models. Furthermore, it is more flexible to take into account the impact of covariates. Copyright © 2013, International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc.

Nonparametric Combinatorial Sequence Models

NASA Astrophysics Data System (ADS)

Wauthier, Fabian L.; Jordan, Michael I.; Jojic, Nebojsa

This work considers biological sequences that exhibit combinatorial structures in their composition: groups of positions of the aligned sequences are "linked" and covary as one unit across sequences. If multiple such groups exist, complex interactions can emerge between them. Sequences of this kind arise frequently in biology but methodologies for analyzing them are still being developed. This paper presents a nonparametric prior on sequences which allows combinatorial structures to emerge and which induces a posterior distribution over factorized sequence representations. We carry out experiments on three sequence datasets which indicate that combinatorial structures are indeed present and that combinatorial sequence models can more succinctly describe them than simpler mixture models. We conclude with an application to MHC binding prediction which highlights the utility of the posterior distribution induced by the prior. By integrating out the posterior our method compares favorably to leading binding predictors.

Non-Parametric Collision Probability for Low-Velocity Encounters

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2007-01-01

An implicit, but not necessarily obvious, assumption in all of the current techniques for assessing satellite collision probability is that the relative position uncertainty is perfectly correlated in time. If there is any mis-modeling of the dynamics in the propagation of the relative position error covariance matrix, time-wise de-correlation of the uncertainty will increase the probability of collision over a given time interval. The paper gives some examples that illustrate this point. This paper argues that, for the present, Monte Carlo analysis is the best available tool for handling low-velocity encounters, and suggests some techniques for addressing the issues just described. One proposal is for the use of a non-parametric technique that is widely used in actuarial and medical studies. The other suggestion is that accurate process noise models be used in the Monte Carlo trials to which the non-parametric estimate is applied. A further contribution of this paper is a description of how the time-wise decorrelation of uncertainty increases the probability of collision.

Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

PubMed

Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi

2015-02-01

We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

A Simulation Study on the Performance of the Simple Difference and Covariance-Adjusted Scores in Randomized Experimental Designs

ERIC Educational Resources Information Center

Petscher, Yaacov; Schatschneider, Christopher

2011-01-01

Research by Huck and McLean (1975) demonstrated that the covariance-adjusted score is more powerful than the simple difference score, yet recent reviews indicate researchers are equally likely to use either score type in two-wave randomized experimental designs. A Monte Carlo simulation was conducted to examine the conditions under which the…

Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife

ERIC Educational Resources Information Center

Jennrich, Robert I.

2008-01-01

The infinitesimal jackknife provides a simple general method for estimating standard errors in covariance structure analysis. Beyond its simplicity and generality what makes the infinitesimal jackknife method attractive is that essentially no assumptions are required to produce consistent standard error estimates, not even the requirement that the…

Robust location and spread measures for nonparametric probability density function estimation.

PubMed

López-Rubio, Ezequiel

2009-10-01

Robustness against outliers is a desirable property of any unsupervised learning scheme. In particular, probability density estimators benefit from incorporating this feature. A possible strategy to achieve this goal is to substitute the sample mean and the sample covariance matrix by more robust location and spread estimators. Here we use the L1-median to develop a nonparametric probability density function (PDF) estimator. We prove its most relevant properties, and we show its performance in density estimation and classification applications.

Robust estimation for partially linear models with large-dimensional covariates.

PubMed

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.

Linkage mapping of beta 2 EEG waves via non-parametric regression.

PubMed

Ghosh, Saurabh; Begleiter, Henri; Porjesz, Bernice; Chorlian, David B; Edenberg, Howard J; Foroud, Tatiana; Goate, Alison; Reich, Theodore

2003-04-01

Parametric linkage methods for analyzing quantitative trait loci are sensitive to violations in trait distributional assumptions. Non-parametric methods are relatively more robust. In this article, we modify the non-parametric regression procedure proposed by Ghosh and Majumder [2000: Am J Hum Genet 66:1046-1061] to map Beta 2 EEG waves using genome-wide data generated in the COGA project. Significant linkage findings are obtained on chromosomes 1, 4, 5, and 15 with findings at multiple regions on chromosomes 4 and 15. We analyze the data both with and without incorporating alcoholism as a covariate. We also test for epistatic interactions between regions of the genome exhibiting significant linkage with the EEG phenotypes and find evidence of epistatic interactions between a region each on chromosome 1 and chromosome 4 with one region on chromosome 15. While regressing out the effect of alcoholism does not affect the linkage findings, the epistatic interactions become statistically insignificant. Copyright 2003 Wiley-Liss, Inc.

Are your covariates under control? How normalization can re-introduce covariate effects.

PubMed

Pain, Oliver; Dudbridge, Frank; Ronald, Angelica

2018-04-30

Many statistical tests rely on the assumption that the residuals of a model are normally distributed. Rank-based inverse normal transformation (INT) of the dependent variable is one of the most popular approaches to satisfy the normality assumption. When covariates are included in the analysis, a common approach is to first adjust for the covariates and then normalize the residuals. This study investigated the effect of regressing covariates against the dependent variable and then applying rank-based INT to the residuals. The correlation between the dependent variable and covariates at each stage of processing was assessed. An alternative approach was tested in which rank-based INT was applied to the dependent variable before regressing covariates. Analyses based on both simulated and real data examples demonstrated that applying rank-based INT to the dependent variable residuals after regressing out covariates re-introduces a linear correlation between the dependent variable and covariates, increasing type-I errors and reducing power. On the other hand, when rank-based INT was applied prior to controlling for covariate effects, residuals were normally distributed and linearly uncorrelated with covariates. This latter approach is therefore recommended in situations were normality of the dependent variable is required.

A nonparametric method to generate synthetic populations to adjust for complex sampling design features.

PubMed

Dong, Qi; Elliott, Michael R; Raghunathan, Trivellore E

2014-06-01

Outside of the survey sampling literature, samples are often assumed to be generated by a simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs.

A nonparametric method to generate synthetic populations to adjust for complex sampling design features

PubMed Central

Dong, Qi; Elliott, Michael R.; Raghunathan, Trivellore E.

2017-01-01

Outside of the survey sampling literature, samples are often assumed to be generated by a simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs. PMID:29200608

Statistical inference based on the nonparametric maximum likelihood estimator under double-truncation.

PubMed

Emura, Takeshi; Konno, Yoshihiko; Michimae, Hirofumi

2015-07-01

Doubly truncated data consist of samples whose observed values fall between the right- and left- truncation limits. With such samples, the distribution function of interest is estimated using the nonparametric maximum likelihood estimator (NPMLE) that is obtained through a self-consistency algorithm. Owing to the complicated asymptotic distribution of the NPMLE, the bootstrap method has been suggested for statistical inference. This paper proposes a closed-form estimator for the asymptotic covariance function of the NPMLE, which is computationally attractive alternative to bootstrapping. Furthermore, we develop various statistical inference procedures, such as confidence interval, goodness-of-fit tests, and confidence bands to demonstrate the usefulness of the proposed covariance estimator. Simulations are performed to compare the proposed method with both the bootstrap and jackknife methods. The methods are illustrated using the childhood cancer dataset.

Continuous Covariate Imbalance and Conditional Power for Clinical Trial Interim Analyses

PubMed Central

Ciolino, Jody D.; Martin, Renee' H.; Zhao, Wenle; Jauch, Edward C.; Hill, Michael D.; Palesch, Yuko Y.

2014-01-01

Oftentimes valid statistical analyses for clinical trials involve adjustment for known influential covariates, regardless of imbalance observed in these covariates at baseline across treatment groups. Thus, it must be the case that valid interim analyses also properly adjust for these covariates. There are situations, however, in which covariate adjustment is not possible, not planned, or simply carries less merit as it makes inferences less generalizable and less intuitive. In this case, covariate imbalance between treatment groups can have a substantial effect on both interim and final primary outcome analyses. This paper illustrates the effect of influential continuous baseline covariate imbalance on unadjusted conditional power (CP), and thus, on trial decisions based on futility stopping bounds. The robustness of the relationship is illustrated for normal, skewed, and bimodal continuous baseline covariates that are related to a normally distributed primary outcome. Results suggest that unadjusted CP calculations in the presence of influential covariate imbalance require careful interpretation and evaluation. PMID:24607294

A Review of DIMPACK Version 1.0: Conditional Covariance-Based Test Dimensionality Analysis Package

ERIC Educational Resources Information Center

Deng, Nina; Han, Kyung T.; Hambleton, Ronald K.

2013-01-01

DIMPACK Version 1.0 for assessing test dimensionality based on a nonparametric conditional covariance approach is reviewed. This software was originally distributed by Assessment Systems Corporation and now can be freely accessed online. The software consists of Windows-based interfaces of three components: DIMTEST, DETECT, and CCPROX/HAC, which…

Varied applications of a new maximum-likelihood code with complete covariance capability. [FERRET, for data adjustment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmittroth, F.

1978-01-01

Applications of a new data-adjustment code are given. The method is based on a maximum-likelihood extension of generalized least-squares methods that allow complete covariance descriptions for the input data and the final adjusted data evaluations. The maximum-likelihood approach is used with a generalized log-normal distribution that provides a way to treat problems with large uncertainties and that circumvents the problem of negative values that can occur for physically positive quantities. The computer code, FERRET, is written to enable the user to apply it to a large variety of problems by modifying only the input subroutine. The following applications are discussed:more » A 75-group a priori damage function is adjusted by as much as a factor of two by use of 14 integral measurements in different reactor spectra. Reactor spectra and dosimeter cross sections are simultaneously adjusted on the basis of both integral measurements and experimental proton-recoil spectra. The simultaneous use of measured reaction rates, measured worths, microscopic measurements, and theoretical models are used to evaluate dosimeter and fission-product cross sections. Applications in the data reduction of neutron cross section measurements and in the evaluation of reactor after-heat are also considered. 6 figures.« less

Covariate Imbalance and Precision in Measuring Treatment Effects

ERIC Educational Resources Information Center

Liu, Xiaofeng Steven

2011-01-01

Covariate adjustment can increase the precision of estimates by removing unexplained variance from the error in randomized experiments, although chance covariate imbalance tends to counteract the improvement in precision. The author develops an easy measure to examine chance covariate imbalance in randomization by standardizing the average…

Robust estimation for partially linear models with large-dimensional covariates

PubMed Central

Zhu, LiPing; Li, RunZe; Cui, HengJian

2014-01-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures. PMID:24955087

Multilevel covariance regression with correlated random effects in the mean and variance structure.

PubMed

Quintero, Adrian; Lesaffre, Emmanuel

2017-09-01

Multivariate regression methods generally assume a constant covariance matrix for the observations. In case a heteroscedastic model is needed, the parametric and nonparametric covariance regression approaches can be restrictive in the literature. We propose a multilevel regression model for the mean and covariance structure, including random intercepts in both components and allowing for correlation between them. The implied conditional covariance function can be different across clusters as a result of the random effect in the variance structure. In addition, allowing for correlation between the random intercepts in the mean and covariance makes the model convenient for skewedly distributed responses. Furthermore, it permits us to analyse directly the relation between the mean response level and the variability in each cluster. Parameter estimation is carried out via Gibbs sampling. We compare the performance of our model to other covariance modelling approaches in a simulation study. Finally, the proposed model is applied to the RN4CAST dataset to identify the variables that impact burnout of nurses in Belgium. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Spatio-Temporal Regression Based Clustering of Precipitation Extremes in a Presence of Systematically Missing Covariates

NASA Astrophysics Data System (ADS)

Kaiser, Olga; Martius, Olivia; Horenko, Illia

2017-04-01

Regression based Generalized Pareto Distribution (GPD) models are often used to describe the dynamics of hydrological threshold excesses relying on the explicit availability of all of the relevant covariates. But, in real application the complete set of relevant covariates might be not available. In this context, it was shown that under weak assumptions the influence coming from systematically missing covariates can be reflected by a nonstationary and nonhomogenous dynamics. We present a data-driven, semiparametric and an adaptive approach for spatio-temporal regression based clustering of threshold excesses in a presence of systematically missing covariates. The nonstationary and nonhomogenous behavior of threshold excesses is describes by a set of local stationary GPD models, where the parameters are expressed as regression models, and a non-parametric spatio-temporal hidden switching process. Exploiting nonparametric Finite Element time-series analysis Methodology (FEM) with Bounded Variation of the model parameters (BV) for resolving the spatio-temporal switching process, the approach goes beyond strong a priori assumptions made is standard latent class models like Mixture Models and Hidden Markov Models. Additionally, the presented FEM-BV-GPD provides a pragmatic description of the corresponding spatial dependence structure by grouping together all locations that exhibit similar behavior of the switching process. The performance of the framework is demonstrated on daily accumulated precipitation series over 17 different locations in Switzerland from 1981 till 2013 - showing that the introduced approach allows for a better description of the historical data.

A Semiparametric Approach to Simultaneous Covariance Estimation for Bivariate Sparse Longitudinal Data

PubMed Central

Das, Kiranmoy; Daniels, Michael J.

2014-01-01

Summary Estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications. In addition, when data are collected from several groups over time, it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and/or bias. Nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study. For the irregular case, with longitudinal measurements that are bivariate or multivariate, modeling becomes more difficult. In this article, to model bivariate sparse longitudinal data from several groups, we propose a flexible covariance structure via a novel matrix stick-breaking process for the residual covariance structure and a Dirichlet process mixture of normals for the random effects. Simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches. We also analyze a subset of Framingham Heart Study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different BMI groups (high, medium and low) at baseline. PMID:24400941

A Comparison of Bias Correction Adjustments for the DETECT Procedure

ERIC Educational Resources Information Center

Nandakumar, Ratna; Yu, Feng; Zhang, Yanwei

2011-01-01

DETECT is a nonparametric methodology to identify the dimensional structure underlying test data. The associated DETECT index, "D[subscript max]," denotes the degree of multidimensionality in data. Conditional covariances (CCOV) are the building blocks of this index. In specifying population CCOVs, the latent test composite [theta][subscript TT]…

Essays in applied macroeconomics: Asymmetric price adjustment, exchange rate and treatment effect

NASA Astrophysics Data System (ADS)

Gu, Jingping

This dissertation consists of three essays. Chapter II examines the possible asymmetric response of gasoline prices to crude oil price changes using an error correction model with GARCH errors. Recent papers have looked at this issue. Some of these papers estimate a form of error correction model, but none of them accounts for autoregressive heteroskedasticity in estimation and testing for asymmetry and none of them takes the response of crude oil price into consideration. We find that time-varying volatility of gasoline price disturbances is an important feature of the data, and when we allow for asymmetric GARCH errors and investigate the system wide impulse response function, we find evidence of asymmetric adjustment to crude oil price changes in weekly retail gasoline prices. Chapter III discusses the relationship between fiscal deficit and exchange rate. Economic theory predicts that fiscal deficits can significantly affect real exchange rate movements, but existing empirical evidence reports only a weak impact of fiscal deficits on exchange rates. Based on US dollar-based real exchange rates in G5 countries and a flexible varying coefficient model, we show that the previously documented weak relationship between fiscal deficits and exchange rates may be the result of additive specifications, and that the relationship is stronger if we allow fiscal deficits to impact real exchange rates non-additively as well as nonlinearly. We find that the speed of exchange rate adjustment toward equilibrium depends on the state of the fiscal deficit; a fiscal contraction in the US can lead to less persistence in the deviation of exchange rates from fundamentals, and faster mean reversion to the equilibrium. Chapter IV proposes a kernel method to deal with the nonparametric regression model with only discrete covariates as regressors. This new approach is based on recently developed least squares cross-validation kernel smoothing method. It can not only automatically smooth

Multiple Imputation of a Randomly Censored Covariate Improves Logistic Regression Analysis.

PubMed

Atem, Folefac D; Qian, Jing; Maye, Jacqueline E; Johnson, Keith A; Betensky, Rebecca A

2016-01-01

Randomly censored covariates arise frequently in epidemiologic studies. The most commonly used methods, including complete case and single imputation or substitution, suffer from inefficiency and bias. They make strong parametric assumptions or they consider limit of detection censoring only. We employ multiple imputation, in conjunction with semi-parametric modeling of the censored covariate, to overcome these shortcomings and to facilitate robust estimation. We develop a multiple imputation approach for randomly censored covariates within the framework of a logistic regression model. We use the non-parametric estimate of the covariate distribution or the semiparametric Cox model estimate in the presence of additional covariates in the model. We evaluate this procedure in simulations, and compare its operating characteristics to those from the complete case analysis and a survival regression approach. We apply the procedures to an Alzheimer's study of the association between amyloid positivity and maternal age of onset of dementia. Multiple imputation achieves lower standard errors and higher power than the complete case approach under heavy and moderate censoring and is comparable under light censoring. The survival regression approach achieves the highest power among all procedures, but does not produce interpretable estimates of association. Multiple imputation offers a favorable alternative to complete case analysis and ad hoc substitution methods in the presence of randomly censored covariates within the framework of logistic regression.

Understanding Past Population Dynamics: Bayesian Coalescent-Based Modeling with Covariates

PubMed Central

Gill, Mandev S.; Lemey, Philippe; Bennett, Shannon N.; Biek, Roman; Suchard, Marc A.

2016-01-01

Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman’s coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late

SEMIPARAMETRIC QUANTILE REGRESSION WITH HIGH-DIMENSIONAL COVARIATES

PubMed Central

Zhu, Liping; Huang, Mian; Li, Runze

2012-01-01

This paper is concerned with quantile regression for a semiparametric regression model, in which both the conditional mean and conditional variance function of the response given the covariates admit a single-index structure. This semiparametric regression model enables us to reduce the dimension of the covariates and simultaneously retains the flexibility of nonparametric regression. Under mild conditions, we show that the simple linear quantile regression offers a consistent estimate of the index parameter vector. This is a surprising and interesting result because the single-index model is possibly misspecified under the linear quantile regression. With a root-n consistent estimate of the index vector, one may employ a local polynomial regression technique to estimate the conditional quantile function. This procedure is computationally efficient, which is very appealing in high-dimensional data analysis. We show that the resulting estimator of the quantile function performs asymptotically as efficiently as if the true value of the index vector were known. The methodologies are demonstrated through comprehensive simulation studies and an application to a real dataset. PMID:24501536

Measuring continuous baseline covariate imbalances in clinical trial data

PubMed Central

Ciolino, Jody D.; Martin, Renee’ H.; Zhao, Wenle; Hill, Michael D.; Jauch, Edward C.; Palesch, Yuko Y.

2014-01-01

This paper presents and compares several methods of measuring continuous baseline covariate imbalance in clinical trial data. Simulations illustrate that though the t-test is an inappropriate method of assessing continuous baseline covariate imbalance, the test statistic itself is a robust measure in capturing imbalance in continuous covariate distributions. Guidelines to assess effects of imbalance on bias, type I error rate, and power for hypothesis test for treatment effect on continuous outcomes are presented, and the benefit of covariate-adjusted analysis (ANCOVA) is also illustrated. PMID:21865270

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

NASA Astrophysics Data System (ADS)

Schiemann, R.; Erdin, R.; Willi, M.; Frei, C.; Berenguer, M.; Sempere-Torres, D.

2011-05-01

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

NASA Astrophysics Data System (ADS)

Schiemann, R.; Erdin, R.; Willi, M.; Frei, C.; Berenguer, M.; Sempere-Torres, D.

2010-09-01

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation

How large are the consequences of covariate imbalance in cluster randomized trials: a simulation study with a continuous outcome and a binary covariate at the cluster level.

PubMed

Moerbeek, Mirjam; van Schie, Sander

2016-07-11

The number of clusters in a cluster randomized trial is often low. It is therefore likely random assignment of clusters to treatment conditions results in covariate imbalance. There are no studies that quantify the consequences of covariate imbalance in cluster randomized trials on parameter and standard error bias and on power to detect treatment effects. The consequences of covariance imbalance in unadjusted and adjusted linear mixed models are investigated by means of a simulation study. The factors in this study are the degree of imbalance, the covariate effect size, the cluster size and the intraclass correlation coefficient. The covariate is binary and measured at the cluster level; the outcome is continuous and measured at the individual level. The results show covariate imbalance results in negligible parameter bias and small standard error bias in adjusted linear mixed models. Ignoring the possibility of covariate imbalance while calculating the sample size at the cluster level may result in a loss in power of at most 25 % in the adjusted linear mixed model. The results are more severe for the unadjusted linear mixed model: parameter biases up to 100 % and standard error biases up to 200 % may be observed. Power levels based on the unadjusted linear mixed model are often too low. The consequences are most severe for large clusters and/or small intraclass correlation coefficients since then the required number of clusters to achieve a desired power level is smallest. The possibility of covariate imbalance should be taken into account while calculating the sample size of a cluster randomized trial. Otherwise more sophisticated methods to randomize clusters to treatments should be used, such as stratification or balance algorithms. All relevant covariates should be carefully identified, be actually measured and included in the statistical model to avoid severe levels of parameter and standard error bias and insufficient power levels.

Covariance specification and estimation to improve top-down Green House Gas emission estimates

NASA Astrophysics Data System (ADS)

Ghosh, S.; Lopez-Coto, I.; Prasad, K.; Whetstone, J. R.

2015-12-01

accuracy, we perform a sensitivity study to further tune covariance parameters. Finally, we introduce a shrinkage based sample covariance estimation technique for both prior and mismatch covariances. This technique allows us to achieve similar accuracy nonparametrically in a more efficient and automated way.

Bootstrap-based procedures for inference in nonparametric receiver-operating characteristic curve regression analysis.

PubMed

Rodríguez-Álvarez, María Xosé; Roca-Pardiñas, Javier; Cadarso-Suárez, Carmen; Tahoces, Pablo G

2018-03-01

Prior to using a diagnostic test in a routine clinical setting, the rigorous evaluation of its diagnostic accuracy is essential. The receiver-operating characteristic curve is the measure of accuracy most widely used for continuous diagnostic tests. However, the possible impact of extra information about the patient (or even the environment) on diagnostic accuracy also needs to be assessed. In this paper, we focus on an estimator for the covariate-specific receiver-operating characteristic curve based on direct regression modelling and nonparametric smoothing techniques. This approach defines the class of generalised additive models for the receiver-operating characteristic curve. The main aim of the paper is to offer new inferential procedures for testing the effect of covariates on the conditional receiver-operating characteristic curve within the above-mentioned class. Specifically, two different bootstrap-based tests are suggested to check (a) the possible effect of continuous covariates on the receiver-operating characteristic curve and (b) the presence of factor-by-curve interaction terms. The validity of the proposed bootstrap-based procedures is supported by simulations. To facilitate the application of these new procedures in practice, an R-package, known as npROCRegression, is provided and briefly described. Finally, data derived from a computer-aided diagnostic system for the automatic detection of tumour masses in breast cancer is analysed.

A Machine Learning Framework for Plan Payment Risk Adjustment.

PubMed

Rose, Sherri

2016-12-01

To introduce cross-validation and a nonparametric machine learning framework for plan payment risk adjustment and then assess whether they have the potential to improve risk adjustment. 2011-2012 Truven MarketScan database. We compare the performance of multiple statistical approaches within a broad machine learning framework for estimation of risk adjustment formulas. Total annual expenditure was predicted using age, sex, geography, inpatient diagnoses, and hierarchical condition category variables. The methods included regression, penalized regression, decision trees, neural networks, and an ensemble super learner, all in concert with screening algorithms that reduce the set of variables considered. The performance of these methods was compared based on cross-validated R 2 . Our results indicate that a simplified risk adjustment formula selected via this nonparametric framework maintains much of the efficiency of a traditional larger formula. The ensemble approach also outperformed classical regression and all other algorithms studied. The implementation of cross-validated machine learning techniques provides novel insight into risk adjustment estimation, possibly allowing for a simplified formula, thereby reducing incentives for increased coding intensity as well as the ability of insurers to "game" the system with aggressive diagnostic upcoding. © Health Research and Educational Trust.

Improving mass-univariate analysis of neuroimaging data by modelling important unknown covariates: Application to Epigenome-Wide Association Studies.

PubMed

Guillaume, Bryan; Wang, Changqing; Poh, Joann; Shen, Mo Jun; Ong, Mei Lyn; Tan, Pei Fang; Karnani, Neerja; Meaney, Michael; Qiu, Anqi

2018-06-01

Statistical inference on neuroimaging data is often conducted using a mass-univariate model, equivalent to fitting a linear model at every voxel with a known set of covariates. Due to the large number of linear models, it is challenging to check if the selection of covariates is appropriate and to modify this selection adequately. The use of standard diagnostics, such as residual plotting, is clearly not practical for neuroimaging data. However, the selection of covariates is crucial for linear regression to ensure valid statistical inference. In particular, the mean model of regression needs to be reasonably well specified. Unfortunately, this issue is often overlooked in the field of neuroimaging. This study aims to adopt the existing Confounder Adjusted Testing and Estimation (CATE) approach and to extend it for use with neuroimaging data. We propose a modification of CATE that can yield valid statistical inferences using Principal Component Analysis (PCA) estimators instead of Maximum Likelihood (ML) estimators. We then propose a non-parametric hypothesis testing procedure that can improve upon parametric testing. Monte Carlo simulations show that the modification of CATE allows for more accurate modelling of neuroimaging data and can in turn yield a better control of False Positive Rate (FPR) and Family-Wise Error Rate (FWER). We demonstrate its application to an Epigenome-Wide Association Study (EWAS) on neonatal brain imaging and umbilical cord DNA methylation data obtained as part of a longitudinal cohort study. Software for this CATE study is freely available at http://www.bioeng.nus.edu.sg/cfa/Imaging_Genetics2.html. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

Out-of-Sample Extensions for Non-Parametric Kernel Methods.

PubMed

Pan, Binbin; Chen, Wen-Sheng; Chen, Bo; Xu, Chen; Lai, Jianhuang

2017-02-01

Choosing suitable kernels plays an important role in the performance of kernel methods. Recently, a number of studies were devoted to developing nonparametric kernels. Without assuming any parametric form of the target kernel, nonparametric kernel learning offers a flexible scheme to utilize the information of the data, which may potentially characterize the data similarity better. The kernel methods using nonparametric kernels are referred to as nonparametric kernel methods. However, many nonparametric kernel methods are restricted to transductive learning, where the prediction function is defined only over the data points given beforehand. They have no straightforward extension for the out-of-sample data points, and thus cannot be applied to inductive learning. In this paper, we show how to make the nonparametric kernel methods applicable to inductive learning. The key problem of out-of-sample extension is how to extend the nonparametric kernel matrix to the corresponding kernel function. A regression approach in the hyper reproducing kernel Hilbert space is proposed to solve this problem. Empirical results indicate that the out-of-sample performance is comparable to the in-sample performance in most cases. Experiments on face recognition demonstrate the superiority of our nonparametric kernel method over the state-of-the-art parametric kernel methods.

Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aghamousa, Amir; Shafieloo, Arman; Arjunwadkar, Mihir

2015-02-01

Estimation of the angular power spectrum is one of the important steps in Cosmic Microwave Background (CMB) data analysis. Here, we present a nonparametric estimate of the temperature angular power spectrum for the Planck 2013 CMB data. The method implemented in this work is model-independent, and allows the data, rather than the model, to dictate the fit. Since one of the main targets of our analysis is to test the consistency of the ΛCDM model with Planck 2013 data, we use the nuisance parameters associated with the best-fit ΛCDM angular power spectrum to remove foreground contributions from the data atmore » multipoles ℓ ≥50. We thus obtain a combined angular power spectrum data set together with the full covariance matrix, appropriately weighted over frequency channels. Our subsequent nonparametric analysis resolves six peaks (and five dips) up to ℓ ∼1850 in the temperature angular power spectrum. We present uncertainties in the peak/dip locations and heights at the 95% confidence level. We further show how these reflect the harmonicity of acoustic peaks, and can be used for acoustic scale estimation. Based on this nonparametric formalism, we found the best-fit ΛCDM model to be at 36% confidence distance from the center of the nonparametric confidence set—this is considerably larger than the confidence distance (9%) derived earlier from a similar analysis of the WMAP 7-year data. Another interesting result of our analysis is that at low multipoles, the Planck data do not suggest any upturn, contrary to the expectation based on the integrated Sachs-Wolfe contribution in the best-fit ΛCDM cosmology.« less

A new approach to correct the QT interval for changes in heart rate using a nonparametric regression model in beagle dogs.

PubMed

Watanabe, Hiroyuki; Miyazaki, Hiroyasu

2006-01-01

Over- and/or under-correction of QT intervals for changes in heart rate may lead to misleading conclusions and/or masking the potential of a drug to prolong the QT interval. This study examines a nonparametric regression model (Loess Smoother) to adjust the QT interval for differences in heart rate, with an improved fitness over a wide range of heart rates. 240 sets of (QT, RR) observations collected from each of 8 conscious and non-treated beagle dogs were used as the materials for investigation. The fitness of the nonparametric regression model to the QT-RR relationship was compared with four models (individual linear regression, common linear regression, and Bazett's and Fridericia's correlation models) with reference to Akaike's Information Criterion (AIC). Residuals were visually assessed. The bias-corrected AIC of the nonparametric regression model was the best of the models examined in this study. Although the parametric models did not fit, the nonparametric regression model improved the fitting at both fast and slow heart rates. The nonparametric regression model is the more flexible method compared with the parametric method. The mathematical fit for linear regression models was unsatisfactory at both fast and slow heart rates, while the nonparametric regression model showed significant improvement at all heart rates in beagle dogs.

Nonparametric Transfer Function Models

PubMed Central

Liu, Jun M.; Chen, Rong; Yao, Qiwei

2009-01-01

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example. PMID:20628584

AFCI-2.0 Library of Neutron Cross Section Covariances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herman, M.; Herman,M.; Oblozinsky,P.

2011-06-26

Neutron cross section covariance library has been under development by BNL-LANL collaborative effort over the last three years. The primary purpose of the library is to provide covariances for the Advanced Fuel Cycle Initiative (AFCI) data adjustment project, which is focusing on the needs of fast advanced burner reactors. The covariances refer to central values given in the 2006 release of the U.S. neutron evaluated library ENDF/B-VII. The preliminary version (AFCI-2.0beta) has been completed in October 2010 and made available to the users for comments. In the final 2.0 release, covariances for a few materials were updated, in particular newmore » LANL evaluations for {sup 238,240}Pu and {sup 241}Am were adopted. BNL was responsible for covariances for structural materials and fission products, management of the library and coordination of the work, while LANL was in charge of covariances for light nuclei and for actinides.« less

Meta-analysis of Diagnostic Accuracy and ROC Curves with Covariate Adjusted Semiparametric Mixtures.

PubMed

Doebler, Philipp; Holling, Heinz

2015-12-01

Many screening tests dichotomize a measurement to classify subjects. Typically a cut-off value is chosen in a way that allows identification of an acceptable number of cases relative to a reference procedure, but does not produce too many false positives at the same time. Thus for the same sample many pairs of sensitivities and false positive rates result as the cut-off is varied. The curve of these points is called the receiver operating characteristic (ROC) curve. One goal of diagnostic meta-analysis is to integrate ROC curves and arrive at a summary ROC (SROC) curve. Holling, Böhning, and Böhning (Psychometrika 77:106-126, 2012a) demonstrated that finite semiparametric mixtures can describe the heterogeneity in a sample of Lehmann ROC curves well; this approach leads to clusters of SROC curves of a particular shape. We extend this work with the help of the [Formula: see text] transformation, a flexible family of transformations for proportions. A collection of SROC curves is constructed that approximately contains the Lehmann family but in addition allows the modeling of shapes beyond the Lehmann ROC curves. We introduce two rationales for determining the shape from the data. Using the fact that each curve corresponds to a natural univariate measure of diagnostic accuracy, we show how covariate adjusted mixtures lead to a meta-regression on SROC curves. Three worked examples illustrate the method.

Missing continuous outcomes under covariate dependent missingness in cluster randomised trials

PubMed Central

Diaz-Ordaz, Karla; Bartlett, Jonathan W

2016-01-01

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group. PMID:27177885

Missing continuous outcomes under covariate dependent missingness in cluster randomised trials.

PubMed

Hossain, Anower; Diaz-Ordaz, Karla; Bartlett, Jonathan W

2017-06-01

Attrition is a common occurrence in cluster randomised trials which leads to missing outcome data. Two approaches for analysing such trials are cluster-level analysis and individual-level analysis. This paper compares the performance of unadjusted cluster-level analysis, baseline covariate adjusted cluster-level analysis and linear mixed model analysis, under baseline covariate dependent missingness in continuous outcomes, in terms of bias, average estimated standard error and coverage probability. The methods of complete records analysis and multiple imputation are used to handle the missing outcome data. We considered four scenarios, with the missingness mechanism and baseline covariate effect on outcome either the same or different between intervention groups. We show that both unadjusted cluster-level analysis and baseline covariate adjusted cluster-level analysis give unbiased estimates of the intervention effect only if both intervention groups have the same missingness mechanisms and there is no interaction between baseline covariate and intervention group. Linear mixed model and multiple imputation give unbiased estimates under all four considered scenarios, provided that an interaction of intervention and baseline covariate is included in the model when appropriate. Cluster mean imputation has been proposed as a valid approach for handling missing outcomes in cluster randomised trials. We show that cluster mean imputation only gives unbiased estimates when missingness mechanism is the same between the intervention groups and there is no interaction between baseline covariate and intervention group. Multiple imputation shows overcoverage for small number of clusters in each intervention group.

Double-adjustment in propensity score matching analysis: choosing a threshold for considering residual imbalance.

PubMed

Nguyen, Tri-Long; Collins, Gary S; Spence, Jessica; Daurès, Jean-Pierre; Devereaux, P J; Landais, Paul; Le Manach, Yannick

2017-04-28

Double-adjustment can be used to remove confounding if imbalance exists after propensity score (PS) matching. However, it is not always possible to include all covariates in adjustment. We aimed to find the optimal imbalance threshold for entering covariates into regression. We conducted a series of Monte Carlo simulations on virtual populations of 5,000 subjects. We performed PS 1:1 nearest-neighbor matching on each sample. We calculated standardized mean differences across groups to detect any remaining imbalance in the matched samples. We examined 25 thresholds (from 0.01 to 0.25, stepwise 0.01) for considering residual imbalance. The treatment effect was estimated using logistic regression that contained only those covariates considered to be unbalanced by these thresholds. We showed that regression adjustment could dramatically remove residual confounding bias when it included all of the covariates with a standardized difference greater than 0.10. The additional benefit was negligible when we also adjusted for covariates with less imbalance. We found that the mean squared error of the estimates was minimized under the same conditions. If covariate balance is not achieved, we recommend reiterating PS modeling until standardized differences below 0.10 are achieved on most covariates. In case of remaining imbalance, a double adjustment might be worth considering.

Why preferring parametric forecasting to nonparametric methods?

PubMed

Jabot, Franck

2015-05-07

A recent series of papers by Charles T. Perretti and collaborators have shown that nonparametric forecasting methods can outperform parametric methods in noisy nonlinear systems. Such a situation can arise because of two main reasons: the instability of parametric inference procedures in chaotic systems which can lead to biased parameter estimates, and the discrepancy between the real system dynamics and the modeled one, a problem that Perretti and collaborators call "the true model myth". Should ecologists go on using the demanding parametric machinery when trying to forecast the dynamics of complex ecosystems? Or should they rely on the elegant nonparametric approach that appears so promising? It will be here argued that ecological forecasting based on parametric models presents two key comparative advantages over nonparametric approaches. First, the likelihood of parametric forecasting failure can be diagnosed thanks to simple Bayesian model checking procedures. Second, when parametric forecasting is diagnosed to be reliable, forecasting uncertainty can be estimated on virtual data generated with the fitted to data parametric model. In contrast, nonparametric techniques provide forecasts with unknown reliability. This argumentation is illustrated with the simple theta-logistic model that was previously used by Perretti and collaborators to make their point. It should convince ecologists to stick to standard parametric approaches, until methods have been developed to assess the reliability of nonparametric forecasting. Copyright © 2015 Elsevier Ltd. All rights reserved.

A nonparametric method for assessment of interactions in a median regression model for analyzing right censored data.

PubMed

Lee, MinJae; Rahbar, Mohammad H; Talebi, Hooshang

2018-01-01

We propose a nonparametric test for interactions when we are concerned with investigation of the simultaneous effects of two or more factors in a median regression model with right censored survival data. Our approach is developed to detect interaction in special situations, when the covariates have a finite number of levels with a limited number of observations in each level, and it allows varying levels of variance and censorship at different levels of the covariates. Through simulation studies, we compare the power of detecting an interaction between the study group variable and a covariate using our proposed procedure with that of the Cox Proportional Hazard (PH) model and censored quantile regression model. We also assess the impact of censoring rate and type on the standard error of the estimators of parameters. Finally, we illustrate application of our proposed method to real life data from Prospective Observational Multicenter Major Trauma Transfusion (PROMMTT) study to test an interaction effect between type of injury and study sites using median time for a trauma patient to receive three units of red blood cells. The results from simulation studies indicate that our procedure performs better than both Cox PH model and censored quantile regression model based on statistical power for detecting the interaction, especially when the number of observations is small. It is also relatively less sensitive to censoring rates or even the presence of conditionally independent censoring that is conditional on the levels of covariates.

Rediscovery of Good-Turing estimators via Bayesian nonparametrics.

PubMed

Favaro, Stefano; Nipoti, Bernardo; Teh, Yee Whye

2016-03-01

The problem of estimating discovery probabilities originated in the context of statistical ecology, and in recent years it has become popular due to its frequent appearance in challenging applications arising in genetics, bioinformatics, linguistics, designs of experiments, machine learning, etc. A full range of statistical approaches, parametric and nonparametric as well as frequentist and Bayesian, has been proposed for estimating discovery probabilities. In this article, we investigate the relationships between the celebrated Good-Turing approach, which is a frequentist nonparametric approach developed in the 1940s, and a Bayesian nonparametric approach recently introduced in the literature. Specifically, under the assumption of a two parameter Poisson-Dirichlet prior, we show that Bayesian nonparametric estimators of discovery probabilities are asymptotically equivalent, for a large sample size, to suitably smoothed Good-Turing estimators. As a by-product of this result, we introduce and investigate a methodology for deriving exact and asymptotic credible intervals to be associated with the Bayesian nonparametric estimators of discovery probabilities. The proposed methodology is illustrated through a comprehensive simulation study and the analysis of Expressed Sequence Tags data generated by sequencing a benchmark complementary DNA library. © 2015, The International Biometric Society.

Nonparametric Estimation of the Probability of Ruin.

DTIC Science & Technology

1985-02-01

MATHEMATICS RESEARCH CENTER I E N FREES FEB 85 MRC/TSR...in NONPARAMETRIC ESTIMATION OF THE PROBABILITY OF RUIN Lf Edward W. Frees * Mathematics Research Center University of Wisconsin-Madison 610 Walnut...34 - .. --- - • ’. - -:- - - ..- . . .- -- .-.-. . -. . .- •. . - . . - . . .’ . ’- - .. -’vi . .-" "-- -" ,’- UNIVERSITY OF WISCONSIN-MADISON MATHEMATICS RESEARCH CENTER NONPARAMETRIC ESTIMATION OF THE PROBABILITY

The effect of covariate mean differences on the standard error and confidence interval for the comparison of treatment means.

PubMed

Liu, Xiaofeng Steven

2011-05-01

The use of covariates is commonly believed to reduce the unexplained error variance and the standard error for the comparison of treatment means, but the reduction in the standard error is neither guaranteed nor uniform over different sample sizes. The covariate mean differences between the treatment conditions can inflate the standard error of the covariate-adjusted mean difference and can actually produce a larger standard error for the adjusted mean difference than that for the unadjusted mean difference. When the covariate observations are conceived of as randomly varying from one study to another, the covariate mean differences can be related to a Hotelling's T(2) . Using this Hotelling's T(2) statistic, one can always find a minimum sample size to achieve a high probability of reducing the standard error and confidence interval width for the adjusted mean difference. ©2010 The British Psychological Society.

Benchmark dose analysis via nonparametric regression modeling

PubMed Central

Piegorsch, Walter W.; Xiong, Hui; Bhattacharya, Rabi N.; Lin, Lizhen

2013-01-01

Estimation of benchmark doses (BMDs) in quantitative risk assessment traditionally is based upon parametric dose-response modeling. It is a well-known concern, however, that if the chosen parametric model is uncertain and/or misspecified, inaccurate and possibly unsafe low-dose inferences can result. We describe a nonparametric approach for estimating BMDs with quantal-response data based on an isotonic regression method, and also study use of corresponding, nonparametric, bootstrap-based confidence limits for the BMD. We explore the confidence limits’ small-sample properties via a simulation study, and illustrate the calculations with an example from cancer risk assessment. It is seen that this nonparametric approach can provide a useful alternative for BMD estimation when faced with the problem of parametric model uncertainty. PMID:23683057

Threshold regression to accommodate a censored covariate.

PubMed

Qian, Jing; Chiou, Sy Han; Maye, Jacqueline E; Atem, Folefac; Johnson, Keith A; Betensky, Rebecca A

2018-06-22

In several common study designs, regression modeling is complicated by the presence of censored covariates. Examples of such covariates include maternal age of onset of dementia that may be right censored in an Alzheimer's amyloid imaging study of healthy subjects, metabolite measurements that are subject to limit of detection censoring in a case-control study of cardiovascular disease, and progressive biomarkers whose baseline values are of interest, but are measured post-baseline in longitudinal neuropsychological studies of Alzheimer's disease. We propose threshold regression approaches for linear regression models with a covariate that is subject to random censoring. Threshold regression methods allow for immediate testing of the significance of the effect of a censored covariate. In addition, they provide for unbiased estimation of the regression coefficient of the censored covariate. We derive the asymptotic properties of the resulting estimators under mild regularity conditions. Simulations demonstrate that the proposed estimators have good finite-sample performance, and often offer improved efficiency over existing methods. We also derive a principled method for selection of the threshold. We illustrate the approach in application to an Alzheimer's disease study that investigated brain amyloid levels in older individuals, as measured through positron emission tomography scans, as a function of maternal age of dementia onset, with adjustment for other covariates. We have developed an R package, censCov, for implementation of our method, available at CRAN. © 2018, The International Biometric Society.

Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting

PubMed Central

Chan, Kwun Chuen Gary; Yam, Sheung Chi Phillip; Zhang, Zheng

2015-01-01

Summary The estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks. Existing globally efficient estimators require non-parametric estimation of a propensity score function, an outcome regression function or both, but their performance can be poor in practical sample sizes. Without explicitly estimating either functions, we consider a wide class calibration weights constructed to attain an exact three-way balance of the moments of observed covariates among the treated, the control, and the combined group. The wide class includes exponential tilting, empirical likelihood and generalized regression as important special cases, and extends survey calibration estimators to different statistical problems and with important distinctions. Global semiparametric efficiency for the estimation of average treatment effects is established for this general class of calibration estimators. The results show that efficiency can be achieved by solely balancing the covariate distributions without resorting to direct estimation of propensity score or outcome regression function. We also propose a consistent estimator for the efficient asymptotic variance, which does not involve additional functional estimation of either the propensity score or the outcome regression functions. The proposed variance estimator outperforms existing estimators that require a direct approximation of the efficient influence function. PMID:27346982

Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting.

PubMed

Chan, Kwun Chuen Gary; Yam, Sheung Chi Phillip; Zhang, Zheng

2016-06-01

The estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks. Existing globally efficient estimators require non-parametric estimation of a propensity score function, an outcome regression function or both, but their performance can be poor in practical sample sizes. Without explicitly estimating either functions, we consider a wide class calibration weights constructed to attain an exact three-way balance of the moments of observed covariates among the treated, the control, and the combined group. The wide class includes exponential tilting, empirical likelihood and generalized regression as important special cases, and extends survey calibration estimators to different statistical problems and with important distinctions. Global semiparametric efficiency for the estimation of average treatment effects is established for this general class of calibration estimators. The results show that efficiency can be achieved by solely balancing the covariate distributions without resorting to direct estimation of propensity score or outcome regression function. We also propose a consistent estimator for the efficient asymptotic variance, which does not involve additional functional estimation of either the propensity score or the outcome regression functions. The proposed variance estimator outperforms existing estimators that require a direct approximation of the efficient influence function.

Nonparametric estimation and testing of fixed effects panel data models

PubMed Central

Henderson, Daniel J.; Carroll, Raymond J.; Li, Qi

2009-01-01

In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We introduce an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for testing the null hypothesis of random effects against fixed effects in a nonparametric panel data regression model. Simulations are used to examine the finite sample performance of the proposed estimators and the test statistics. PMID:19444335

Nonparametric regression applied to quantitative structure-activity relationships

PubMed

Constans; Hirst

2000-03-01

Several nonparametric regressors have been applied to modeling quantitative structure-activity relationship (QSAR) data. The simplest regressor, the Nadaraya-Watson, was assessed in a genuine multivariate setting. Other regressors, the local linear and the shifted Nadaraya-Watson, were implemented within additive models--a computationally more expedient approach, better suited for low-density designs. Performances were benchmarked against the nonlinear method of smoothing splines. A linear reference point was provided by multilinear regression (MLR). Variable selection was explored using systematic combinations of different variables and combinations of principal components. For the data set examined, 47 inhibitors of dopamine beta-hydroxylase, the additive nonparametric regressors have greater predictive accuracy (as measured by the mean absolute error of the predictions or the Pearson correlation in cross-validation trails) than MLR. The use of principal components did not improve the performance of the nonparametric regressors over use of the original descriptors, since the original descriptors are not strongly correlated. It remains to be seen if the nonparametric regressors can be successfully coupled with better variable selection and dimensionality reduction in the context of high-dimensional QSARs.

Comparing two correlated C indices with right-censored survival outcome: a one-shot nonparametric approach

PubMed Central

Kang, Le; Chen, Weijie; Petrick, Nicholas A.; Gallas, Brandon D.

2014-01-01

The area under the receiver operating characteristic (ROC) curve (AUC) is often used as a summary index of the diagnostic ability in evaluating biomarkers when the clinical outcome (truth) is binary. When the clinical outcome is right-censored survival time, the C index, motivated as an extension of AUC, has been proposed by Harrell as a measure of concordance between a predictive biomarker and the right-censored survival outcome. In this work, we investigate methods for statistical comparison of two diagnostic or predictive systems, of which they could either be two biomarkers or two fixed algorithms, in terms of their C indices. We adopt a U-statistics based C estimator that is asymptotically normal and develop a nonparametric analytical approach to estimate the variance of the C estimator and the covariance of two C estimators. A z-score test is then constructed to compare the two C indices. We validate our one-shot nonparametric method via simulation studies in terms of the type I error rate and power. We also compare our one-shot method with resampling methods including the jackknife and the bootstrap. Simulation results show that the proposed one-shot method provides almost unbiased variance estimations and has satisfactory type I error control and power. Finally, we illustrate the use of the proposed method with an example from the Framingham Heart Study. PMID:25399736

An evaluation of bias in propensity score-adjusted non-linear regression models.

PubMed

Wan, Fei; Mitra, Nandita

2018-03-01

Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

Surface Estimation, Variable Selection, and the Nonparametric Oracle Property.

PubMed

Storlie, Curtis B; Bondell, Howard D; Reich, Brian J; Zhang, Hao Helen

2011-04-01

Variable selection for multivariate nonparametric regression is an important, yet challenging, problem due, in part, to the infinite dimensionality of the function space. An ideal selection procedure should be automatic, stable, easy to use, and have desirable asymptotic properties. In particular, we define a selection procedure to be nonparametric oracle (np-oracle) if it consistently selects the correct subset of predictors and at the same time estimates the smooth surface at the optimal nonparametric rate, as the sample size goes to infinity. In this paper, we propose a model selection procedure for nonparametric models, and explore the conditions under which the new method enjoys the aforementioned properties. Developed in the framework of smoothing spline ANOVA, our estimator is obtained via solving a regularization problem with a novel adaptive penalty on the sum of functional component norms. Theoretical properties of the new estimator are established. Additionally, numerous simulated and real examples further demonstrate that the new approach substantially outperforms other existing methods in the finite sample setting.

A nonparametric spatial scan statistic for continuous data.

PubMed

Jung, Inkyung; Cho, Ho Jin

2015-10-20

Spatial scan statistics are widely used for spatial cluster detection, and several parametric models exist. For continuous data, a normal-based scan statistic can be used. However, the performance of the model has not been fully evaluated for non-normal data. We propose a nonparametric spatial scan statistic based on the Wilcoxon rank-sum test statistic and compared the performance of the method with parametric models via a simulation study under various scenarios. The nonparametric method outperforms the normal-based scan statistic in terms of power and accuracy in almost all cases under consideration in the simulation study. The proposed nonparametric spatial scan statistic is therefore an excellent alternative to the normal model for continuous data and is especially useful for data following skewed or heavy-tailed distributions.

Inadequacy of internal covariance estimation for super-sample covariance

NASA Astrophysics Data System (ADS)

Lacasa, Fabien; Kunz, Martin

2017-08-01

We give an analytical interpretation of how subsample-based internal covariance estimators lead to biased estimates of the covariance, due to underestimating the super-sample covariance (SSC). This includes the jackknife and bootstrap methods as estimators for the full survey area, and subsampling as an estimator of the covariance of subsamples. The limitations of the jackknife covariance have been previously presented in the literature because it is effectively a rescaling of the covariance of the subsample area. However we point out that subsampling is also biased, but for a different reason: the subsamples are not independent, and the corresponding lack of power results in SSC underprediction. We develop the formalism in the case of cluster counts that allows the bias of each covariance estimator to be exactly predicted. We find significant effects for a small-scale area or when a low number of subsamples is used, with auto-redshift biases ranging from 0.4% to 15% for subsampling and from 5% to 75% for jackknife covariance estimates. The cross-redshift covariance is even more affected; biases range from 8% to 25% for subsampling and from 50% to 90% for jackknife. Owing to the redshift evolution of the probe, the covariances cannot be debiased by a simple rescaling factor, and an exact debiasing has the same requirements as the full SSC prediction. These results thus disfavour the use of internal covariance estimators on data itself or a single simulation, leaving analytical prediction and simulations suites as possible SSC predictors.

Bispectrum supersample covariance

NASA Astrophysics Data System (ADS)

Chan, Kwan Chuen; Moradinezhad Dizgah, Azadeh; Noreña, Jorge

2018-02-01

Modes with wavelengths larger than the survey window can have significant impact on the covariance within the survey window. The supersample covariance has been recognized as an important source of covariance for the power spectrum on small scales, and it can potentially be important for the bispectrum covariance as well. In this paper, using the response function formalism, we model the supersample covariance contributions to the bispectrum covariance and the cross-covariance between the power spectrum and the bispectrum. The supersample covariances due to the long-wavelength density and tidal perturbations are investigated, and the tidal contribution is a few orders of magnitude smaller than the density one because in configuration space the bispectrum estimator involves angular averaging and the tidal response function is anisotropic. The impact of the super-survey modes is quantified using numerical measurements with periodic box and sub-box setups. For the matter bispectrum, the ratio between the supersample covariance correction and the small-scale covariance—which can be computed using a periodic box—is roughly an order of magnitude smaller than that for the matter power spectrum. This is because for the bispectrum, the small-scale non-Gaussian covariance is significantly larger than that for the power spectrum. For the cross-covariance, the supersample covariance is as important as for the power spectrum covariance. The supersample covariance prediction with the halo model response function is in good agreement with numerical results.

Using Analysis of Covariance (ANCOVA) with Fallible Covariates

ERIC Educational Resources Information Center

Culpepper, Steven Andrew; Aguinis, Herman

2011-01-01

Analysis of covariance (ANCOVA) is used widely in psychological research implementing nonexperimental designs. However, when covariates are fallible (i.e., measured with error), which is the norm, researchers must choose from among 3 inadequate courses of action: (a) know that the assumption that covariates are perfectly reliable is violated but…

Surface Estimation, Variable Selection, and the Nonparametric Oracle Property

PubMed Central

Storlie, Curtis B.; Bondell, Howard D.; Reich, Brian J.; Zhang, Hao Helen

2010-01-01

Variable selection for multivariate nonparametric regression is an important, yet challenging, problem due, in part, to the infinite dimensionality of the function space. An ideal selection procedure should be automatic, stable, easy to use, and have desirable asymptotic properties. In particular, we define a selection procedure to be nonparametric oracle (np-oracle) if it consistently selects the correct subset of predictors and at the same time estimates the smooth surface at the optimal nonparametric rate, as the sample size goes to infinity. In this paper, we propose a model selection procedure for nonparametric models, and explore the conditions under which the new method enjoys the aforementioned properties. Developed in the framework of smoothing spline ANOVA, our estimator is obtained via solving a regularization problem with a novel adaptive penalty on the sum of functional component norms. Theoretical properties of the new estimator are established. Additionally, numerous simulated and real examples further demonstrate that the new approach substantially outperforms other existing methods in the finite sample setting. PMID:21603586

Comparing two correlated C indices with right-censored survival outcome: a one-shot nonparametric approach.

PubMed

Kang, Le; Chen, Weijie; Petrick, Nicholas A; Gallas, Brandon D

2015-02-20

The area under the receiver operating characteristic curve is often used as a summary index of the diagnostic ability in evaluating biomarkers when the clinical outcome (truth) is binary. When the clinical outcome is right-censored survival time, the C index, motivated as an extension of area under the receiver operating characteristic curve, has been proposed by Harrell as a measure of concordance between a predictive biomarker and the right-censored survival outcome. In this work, we investigate methods for statistical comparison of two diagnostic or predictive systems, of which they could either be two biomarkers or two fixed algorithms, in terms of their C indices. We adopt a U-statistics-based C estimator that is asymptotically normal and develop a nonparametric analytical approach to estimate the variance of the C estimator and the covariance of two C estimators. A z-score test is then constructed to compare the two C indices. We validate our one-shot nonparametric method via simulation studies in terms of the type I error rate and power. We also compare our one-shot method with resampling methods including the jackknife and the bootstrap. Simulation results show that the proposed one-shot method provides almost unbiased variance estimations and has satisfactory type I error control and power. Finally, we illustrate the use of the proposed method with an example from the Framingham Heart Study. Copyright © 2014 John Wiley & Sons, Ltd.

Mathematical models for nonparametric inferences from line transect data

USGS Publications Warehouse

Burnham, K.P.; Anderson, D.R.

1976-01-01

A general mathematical theory of line transects is develoepd which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(O) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y/r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(O/r).

Estimating restricted mean treatment effects with stacked survival models

PubMed Central

Wey, Andrew; Vock, David M.; Connett, John; Rudser, Kyle

2016-01-01

The difference in restricted mean survival times between two groups is a clinically relevant summary measure. With observational data, there may be imbalances in confounding variables between the two groups. One approach to account for such imbalances is estimating a covariate-adjusted restricted mean difference by modeling the covariate-adjusted survival distribution, and then marginalizing over the covariate distribution. Since the estimator for the restricted mean difference is defined by the estimator for the covariate-adjusted survival distribution, it is natural to expect that a better estimator of the covariate-adjusted survival distribution is associated with a better estimator of the restricted mean difference. We therefore propose estimating restricted mean differences with stacked survival models. Stacked survival models estimate a weighted average of several survival models by minimizing predicted error. By including a range of parametric, semi-parametric, and non-parametric models, stacked survival models can robustly estimate a covariate-adjusted survival distribution and, therefore, the restricted mean treatment effect in a wide range of scenarios. We demonstrate through a simulation study that better performance of the covariate-adjusted survival distribution often leads to better mean-squared error of the restricted mean difference although there are notable exceptions. In addition, we demonstrate that the proposed estimator can perform nearly as well as Cox regression when the proportional hazards assumption is satisfied and significantly better when proportional hazards is violated. Finally, the proposed estimator is illustrated with data from the United Network for Organ Sharing to evaluate post-lung transplant survival between large and small-volume centers. PMID:26934835

A quantile regression model for failure-time data with time-dependent covariates

PubMed Central

Gorfine, Malka; Goldberg, Yair; Ritov, Ya’acov

2017-01-01

Summary Since survival data occur over time, often important covariates that we wish to consider also change over time. Such covariates are referred as time-dependent covariates. Quantile regression offers flexible modeling of survival data by allowing the covariates to vary with quantiles. This article provides a novel quantile regression model accommodating time-dependent covariates, for analyzing survival data subject to right censoring. Our simple estimation technique assumes the existence of instrumental variables. In addition, we present a doubly-robust estimator in the sense of Robins and Rotnitzky (1992, Recovery of information and adjustment for dependent censoring using surrogate markers. In: Jewell, N. P., Dietz, K. and Farewell, V. T. (editors), AIDS Epidemiology. Boston: Birkhaäuser, pp. 297–331.). The asymptotic properties of the estimators are rigorously studied. Finite-sample properties are demonstrated by a simulation study. The utility of the proposed methodology is demonstrated using the Stanford heart transplant dataset. PMID:27485534

Using machine learning to assess covariate balance in matching studies.

PubMed

Linden, Ariel; Yarnold, Paul R

2016-12-01

In order to assess the effectiveness of matching approaches in observational studies, investigators typically present summary statistics for each observed pre-intervention covariate, with the objective of showing that matching reduces the difference in means (or proportions) between groups to as close to zero as possible. In this paper, we introduce a new approach to distinguish between study groups based on their distributions of the covariates using a machine-learning algorithm called optimal discriminant analysis (ODA). Assessing covariate balance using ODA as compared with the conventional method has several key advantages: the ability to ascertain how individuals self-select based on optimal (maximum-accuracy) cut-points on the covariates; the application to any variable metric and number of groups; its insensitivity to skewed data or outliers; and the use of accuracy measures that can be widely applied to all analyses. Moreover, ODA accepts analytic weights, thereby extending the assessment of covariate balance to any study design where weights are used for covariate adjustment. By comparing the two approaches using empirical data, we are able to demonstrate that using measures of classification accuracy as balance diagnostics produces highly consistent results to those obtained via the conventional approach (in our matched-pairs example, ODA revealed a weak statistically significant relationship not detected by the conventional approach). Thus, investigators should consider ODA as a robust complement, or perhaps alternative, to the conventional approach for assessing covariate balance in matching studies. © 2016 John Wiley & Sons, Ltd.

Nonparametric Bayesian Modeling for Automated Database Schema Matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferragut, Erik M; Laska, Jason A

2015-01-01

The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric Bayesian models for each field and compares them by computing the probability that a single model could have generated both fields. Our experiments show that our method is more accurate and faster than the existing instance-based matching algorithms in part because of the use of nonparametric Bayesian models.

Combined Use of Integral Experiments and Covariance Data

NASA Astrophysics Data System (ADS)

Palmiotti, G.; Salvatores, M.; Aliberti, G.; Herman, M.; Hoblit, S. D.; McKnight, R. D.; Obložinský, P.; Talou, P.; Hale, G. M.; Hiruta, H.; Kawano, T.; Mattoon, C. M.; Nobre, G. P. A.; Palumbo, A.; Pigni, M.; Rising, M. E.; Yang, W.-S.; Kahler, A. C.

2014-04-01

In the frame of a US-DOE sponsored project, ANL, BNL, INL and LANL have performed a joint multidisciplinary research activity in order to explore the combined use of integral experiments and covariance data with the objective to both give quantitative indications on possible improvements of the ENDF evaluated data files and to reduce at the same time crucial reactor design parameter uncertainties. Methods that have been developed in the last four decades for the purposes indicated above have been improved by some new developments that benefited also by continuous exchanges with international groups working in similar areas. The major new developments that allowed significant progress are to be found in several specific domains: a) new science-based covariance data; b) integral experiment covariance data assessment and improved experiment analysis, e.g., of sample irradiation experiments; c) sensitivity analysis, where several improvements were necessary despite the generally good understanding of these techniques, e.g., to account for fission spectrum sensitivity; d) a critical approach to the analysis of statistical adjustments performance, both a priori and a posteriori; e) generalization of the assimilation method, now applied for the first time not only to multigroup cross sections data but also to nuclear model parameters (the "consistent" method). This article describes the major results obtained in each of these areas; a large scale nuclear data adjustment, based on the use of approximately one hundred high-accuracy integral experiments, will be reported along with a significant example of the application of the new "consistent" method of data assimilation.

Comparison of bias-corrected covariance estimators for MMRM analysis in longitudinal data with dropouts.

PubMed

Gosho, Masahiko; Hirakawa, Akihiro; Noma, Hisashi; Maruo, Kazushi; Sato, Yasunori

2017-10-01

In longitudinal clinical trials, some subjects will drop out before completing the trial, so their measurements towards the end of the trial are not obtained. Mixed-effects models for repeated measures (MMRM) analysis with "unstructured" (UN) covariance structure are increasingly common as a primary analysis for group comparisons in these trials. Furthermore, model-based covariance estimators have been routinely used for testing the group difference and estimating confidence intervals of the difference in the MMRM analysis using the UN covariance. However, using the MMRM analysis with the UN covariance could lead to convergence problems for numerical optimization, especially in trials with a small-sample size. Although the so-called sandwich covariance estimator is robust to misspecification of the covariance structure, its performance deteriorates in settings with small-sample size. We investigated the performance of the sandwich covariance estimator and covariance estimators adjusted for small-sample bias proposed by Kauermann and Carroll ( J Am Stat Assoc 2001; 96: 1387-1396) and Mancl and DeRouen ( Biometrics 2001; 57: 126-134) fitting simpler covariance structures through a simulation study. In terms of the type 1 error rate and coverage probability of confidence intervals, Mancl and DeRouen's covariance estimator with compound symmetry, first-order autoregressive (AR(1)), heterogeneous AR(1), and antedependence structures performed better than the original sandwich estimator and Kauermann and Carroll's estimator with these structures in the scenarios where the variance increased across visits. The performance based on Mancl and DeRouen's estimator with these structures was nearly equivalent to that based on the Kenward-Roger method for adjusting the standard errors and degrees of freedom with the UN structure. The model-based covariance estimator with the UN structure under unadjustment of the degrees of freedom, which is frequently used in applications

An Empirical Study of Eight Nonparametric Tests in Hierarchical Regression.

ERIC Educational Resources Information Center

Harwell, Michael; Serlin, Ronald C.

When normality does not hold, nonparametric tests represent an important data-analytic alternative to parametric tests. However, the use of nonparametric tests in educational research has been limited by the absence of easily performed tests for complex experimental designs and analyses, such as factorial designs and multiple regression analyses,…

Analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method.

PubMed

Dwivedi, Alok Kumar; Mallawaarachchi, Indika; Alvarado, Luis A

2017-06-30

Experimental studies in biomedical research frequently pose analytical problems related to small sample size. In such studies, there are conflicting findings regarding the choice of parametric and nonparametric analysis, especially with non-normal data. In such instances, some methodologists questioned the validity of parametric tests and suggested nonparametric tests. In contrast, other methodologists found nonparametric tests to be too conservative and less powerful and thus preferred using parametric tests. Some researchers have recommended using a bootstrap test; however, this method also has small sample size limitation. We used a pooled method in nonparametric bootstrap test that may overcome the problem related with small samples in hypothesis testing. The present study compared nonparametric bootstrap test with pooled resampling method corresponding to parametric, nonparametric, and permutation tests through extensive simulations under various conditions and using real data examples. The nonparametric pooled bootstrap t-test provided equal or greater power for comparing two means as compared with unpaired t-test, Welch t-test, Wilcoxon rank sum test, and permutation test while maintaining type I error probability for any conditions except for Cauchy and extreme variable lognormal distributions. In such cases, we suggest using an exact Wilcoxon rank sum test. Nonparametric bootstrap paired t-test also provided better performance than other alternatives. Nonparametric bootstrap test provided benefit over exact Kruskal-Wallis test. We suggest using nonparametric bootstrap test with pooled resampling method for comparing paired or unpaired means and for validating the one way analysis of variance test results for non-normal data in small sample size studies. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Auto covariance computer

NASA Technical Reports Server (NTRS)

Hepner, T. E.; Meyers, J. F. (Inventor)

1985-01-01

A laser velocimeter covariance processor which calculates the auto covariance and cross covariance functions for a turbulent flow field based on Poisson sampled measurements in time from a laser velocimeter is described. The device will process a block of data that is up to 4096 data points in length and return a 512 point covariance function with 48-bit resolution along with a 512 point histogram of the interarrival times which is used to normalize the covariance function. The device is designed to interface and be controlled by a minicomputer from which the data is received and the results returned. A typical 4096 point computation takes approximately 1.5 seconds to receive the data, compute the covariance function, and return the results to the computer.

Estimating the extreme low-temperature event using nonparametric methods

NASA Astrophysics Data System (ADS)

D'Silva, Anisha

This thesis presents a new method of estimating the one-in-N low temperature threshold using a non-parametric statistical method called kernel density estimation applied to daily average wind-adjusted temperatures. We apply our One-in-N Algorithm to local gas distribution companies (LDCs), as they have to forecast the daily natural gas needs of their consumers. In winter, demand for natural gas is high. Extreme low temperature events are not directly related to an LDCs gas demand forecasting, but knowledge of extreme low temperatures is important to ensure that an LDC has enough capacity to meet customer demands when extreme low temperatures are experienced. We present a detailed explanation of our One-in-N Algorithm and compare it to the methods using the generalized extreme value distribution, the normal distribution, and the variance-weighted composite distribution. We show that our One-in-N Algorithm estimates the one-in- N low temperature threshold more accurately than the methods using the generalized extreme value distribution, the normal distribution, and the variance-weighted composite distribution according to root mean square error (RMSE) measure at a 5% level of significance. The One-in- N Algorithm is tested by counting the number of times the daily average wind-adjusted temperature is less than or equal to the one-in- N low temperature threshold.

Adjusting head circumference for covariates in autism: clinical correlates of a highly heritable continuous trait.

PubMed

Chaste, Pauline; Klei, Lambertus; Sanders, Stephan J; Murtha, Michael T; Hus, Vanessa; Lowe, Jennifer K; Willsey, A Jeremy; Moreno-De-Luca, Daniel; Yu, Timothy W; Fombonne, Eric; Geschwind, Daniel; Grice, Dorothy E; Ledbetter, David H; Lord, Catherine; Mane, Shrikant M; Lese Martin, Christa; Martin, Donna M; Morrow, Eric M; Walsh, Christopher A; Sutcliffe, James S; State, Matthew W; Devlin, Bernie; Cook, Edwin H; Kim, Soo-Jeong

2013-10-15

Brain development follows a different trajectory in children with autism spectrum disorders (ASD) than in typically developing children. A proxy for neurodevelopment could be head circumference (HC), but studies assessing HC and its clinical correlates in ASD have been inconsistent. This study investigates HC and clinical correlates in the Simons Simplex Collection cohort. We used a mixed linear model to estimate effects of covariates and the deviation from the expected HC given parental HC (genetic deviation). After excluding individuals with incomplete data, 7225 individuals in 1891 families remained for analysis. We examined the relationship between HC/genetic deviation of HC and clinical parameters. Gender, age, height, weight, genetic ancestry, and ASD status were significant predictors of HC (estimate of the ASD effect = .2 cm). HC was approximately normally distributed in probands and unaffected relatives, with only a few outliers. Genetic deviation of HC was also normally distributed, consistent with a random sampling of parental genes. Whereas larger HC than expected was associated with ASD symptom severity and regression, IQ decreased with the absolute value of the genetic deviation of HC. Measured against expected values derived from covariates of ASD subjects, statistical outliers for HC were uncommon. HC is a strongly heritable trait, and population norms for HC would be far more accurate if covariates including genetic ancestry, height, and age were taken into account. The association of diminishing IQ with absolute deviation from predicted HC values suggests HC could reflect subtle underlying brain development and warrants further investigation. © 2013 Society of Biological Psychiatry.

Adjusting head circumference for covariates in autism: clinical correlates of a highly heritable continuous trait

PubMed Central

Chaste, Pauline; Klei, Lambertus; Sanders, Stephan J.; Murtha, Michael T.; Hus, Vanessa; Lowe, Jennifer K.; Willsey, A. Jeremy; Moreno-De-Luca, Daniel; Yu, Timothy W.; Fombonne, Eric; Geschwind, Daniel; Grice, Dorothy E.; Ledbetter, David H.; Lord, Catherine; Mane, Shrikant M.; Martin, Christa Lese; Martin, Donna M.; Morrow, Eric M.; Walsh, Christopher A.; Sutcliffe, James S.; State, Matthew W.; Devlin, Bernie; Cook, Edwin H.; Kim, Soo-Jeong

2013-01-01

BACKGROUND Brain development follows a different trajectory in children with Autism Spectrum Disorders (ASD) than in typically developing children. A proxy for neurodevelopment could be head circumference (HC), but studies assessing HC and its clinical correlates in ASD have been inconsistent. This study investigates HC and clinical correlates in the Simons Simplex Collection cohort. METHODS We used a mixed linear model to estimate effects of covariates and the deviation from the expected HC given parental HC (genetic deviation). After excluding individuals with incomplete data, 7225 individuals in 1891 families remained for analysis. We examined the relationship between HC/genetic deviation of HC and clinical parameters. RESULTS Gender, age, height, weight, genetic ancestry and ASD status were significant predictors of HC (estimate of the ASD effect=0.2cm). HC was approximately normally distributed in probands and unaffected relatives, with only a few outliers. Genetic deviation of HC was also normally distributed, consistent with a random sampling of parental genes. Whereas larger HC than expected was associated with ASD symptom severity and regression, IQ decreased with the absolute value of the genetic deviation of HC. CONCLUSIONS Measured against expected values derived from covariates of ASD subjects, statistical outliers for HC were uncommon. HC is a strongly heritable trait and population norms for HC would be far more accurate if covariates including genetic ancestry, height and age were taken into account. The association of diminishing IQ with absolute deviation from predicted HC values suggests HC could reflect subtle underlying brain development and warrants further investigation. PMID:23746936

Difficulties with Regression Analysis of Age-Adjusted Rates.

DTIC Science & Technology

1982-09-01

variables used in those analyses, such as death rates in various states, have been age adjusted, whereas the predictor variables have not been age adjusted...The use of crude state death rates as the outcome variable with crude covariates and age as predictors can avoid the problem, at least under some...should be regressed on age-adjusted exposure Z+B+ Although age-specific death rates , Yas+’ may be available, it is often difficult to obtain age

Predicting Market Impact Costs Using Nonparametric Machine Learning Models.

PubMed

Park, Saerom; Lee, Jaewook; Son, Youngdoo

2016-01-01

Market impact cost is the most significant portion of implicit transaction costs that can reduce the overall transaction cost, although it cannot be measured directly. In this paper, we employed the state-of-the-art nonparametric machine learning models: neural networks, Bayesian neural network, Gaussian process, and support vector regression, to predict market impact cost accurately and to provide the predictive model that is versatile in the number of variables. We collected a large amount of real single transaction data of US stock market from Bloomberg Terminal and generated three independent input variables. As a result, most nonparametric machine learning models outperformed a-state-of-the-art benchmark parametric model such as I-star model in four error measures. Although these models encounter certain difficulties in separating the permanent and temporary cost directly, nonparametric machine learning models can be good alternatives in reducing transaction costs by considerably improving in prediction performance.

Mathematical models for non-parametric inferences from line transect data

USGS Publications Warehouse

Burnham, K.P.; Anderson, D.R.

1976-01-01

A general mathematical theory of line transects is developed which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(0) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y I r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(0 I r).

CERAMIC: Case-Control Association Testing in Samples with Related Individuals, Based on Retrospective Mixed Model Analysis with Adjustment for Covariates

PubMed Central

Zhong, Sheng; McPeek, Mary Sara

2016-01-01

We consider the problem of genetic association testing of a binary trait in a sample that contains related individuals, where we adjust for relevant covariates and allow for missing data. We propose CERAMIC, an estimating equation approach that can be viewed as a hybrid of logistic regression and linear mixed-effects model (LMM) approaches. CERAMIC extends the recently proposed CARAT method to allow samples with related individuals and to incorporate partially missing data. In simulations, we show that CERAMIC outperforms existing LMM and generalized LMM approaches, maintaining high power and correct type 1 error across a wider range of scenarios. CERAMIC results in a particularly large power increase over existing methods when the sample includes related individuals with some missing data (e.g., when some individuals with phenotype and covariate information have missing genotype), because CERAMIC is able to make use of the relationship information to incorporate partially missing data in the analysis while correcting for dependence. Because CERAMIC is based on a retrospective analysis, it is robust to misspecification of the phenotype model, resulting in better control of type 1 error and higher power than that of prospective methods, such as GMMAT, when the phenotype model is misspecified. CERAMIC is computationally efficient for genomewide analysis in samples of related individuals of almost any configuration, including small families, unrelated individuals and even large, complex pedigrees. We apply CERAMIC to data on type 2 diabetes (T2D) from the Framingham Heart Study. In a genome scan, 9 of the 10 smallest CERAMIC p-values occur in or near either known T2D susceptibility loci or plausible candidates, verifying that CERAMIC is able to home in on the important loci in a genome scan. PMID:27695091

Design of DNA pooling to allow incorporation of covariates in rare variants analysis.

PubMed

Guan, Weihua; Li, Chun

2014-01-01

Rapid advances in next-generation sequencing technologies facilitate genetic association studies of an increasingly wide array of rare variants. To capture the rare or less common variants, a large number of individuals will be needed. However, the cost of a large scale study using whole genome or exome sequencing is still high. DNA pooling can serve as a cost-effective approach, but with a potential limitation that the identity of individual genomes would be lost and therefore individual characteristics and environmental factors could not be adjusted in association analysis, which may result in power loss and a biased estimate of genetic effect. For case-control studies, we propose a design strategy for pool creation and an analysis strategy that allows covariate adjustment, using multiple imputation technique. Simulations show that our approach can obtain reasonable estimate for genotypic effect with only slight loss of power compared to the much more expensive approach of sequencing individual genomes. Our design and analysis strategies enable more powerful and cost-effective sequencing studies of complex diseases, while allowing incorporation of covariate adjustment.

Predicting Market Impact Costs Using Nonparametric Machine Learning Models

PubMed Central

Park, Saerom; Lee, Jaewook; Son, Youngdoo

2016-01-01

Market impact cost is the most significant portion of implicit transaction costs that can reduce the overall transaction cost, although it cannot be measured directly. In this paper, we employed the state-of-the-art nonparametric machine learning models: neural networks, Bayesian neural network, Gaussian process, and support vector regression, to predict market impact cost accurately and to provide the predictive model that is versatile in the number of variables. We collected a large amount of real single transaction data of US stock market from Bloomberg Terminal and generated three independent input variables. As a result, most nonparametric machine learning models outperformed a-state-of-the-art benchmark parametric model such as I-star model in four error measures. Although these models encounter certain difficulties in separating the permanent and temporary cost directly, nonparametric machine learning models can be good alternatives in reducing transaction costs by considerably improving in prediction performance. PMID:26926235

Nonparametric methods for doubly robust estimation of continuous treatment effects.

PubMed

Kennedy, Edward H; Ma, Zongming; McHugh, Matthew D; Small, Dylan S

2017-09-01

Continuous treatments (e.g., doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We develop a novel kernel smoothing approach that requires only mild smoothness assumptions on the effect curve, and still allows for misspecification of either the treatment density or outcome regression. We derive asymptotic properties and give a procedure for data-driven bandwidth selection. The methods are illustrated via simulation and in a study of the effect of nurse staffing on hospital readmissions penalties.

Baseline adjustments for binary data in repeated cross-sectional cluster randomized trials.

PubMed

Nixon, R M; Thompson, S G

2003-09-15

Analysis of covariance models, which adjust for a baseline covariate, are often used to compare treatment groups in a controlled trial in which individuals are randomized. Such analysis adjusts for any baseline imbalance and usually increases the precision of the treatment effect estimate. We assess the value of such adjustments in the context of a cluster randomized trial with repeated cross-sectional design and a binary outcome. In such a design, a new sample of individuals is taken from the clusters at each measurement occasion, so that baseline adjustment has to be at the cluster level. Logistic regression models are used to analyse the data, with cluster level random effects to allow for different outcome probabilities in each cluster. We compare the estimated treatment effect and its precision in models that incorporate a covariate measuring the cluster level probabilities at baseline and those that do not. In two data sets, taken from a cluster randomized trial in the treatment of menorrhagia, the value of baseline adjustment is only evident when the number of subjects per cluster is large. We assess the generalizability of these findings by undertaking a simulation study, and find that increased precision of the treatment effect requires both large cluster sizes and substantial heterogeneity between clusters at baseline, but baseline imbalance arising by chance in a randomized study can always be effectively adjusted for. Copyright 2003 John Wiley & Sons, Ltd.

The relationship between multilevel models and non-parametric multilevel mixture models: Discrete approximation of intraclass correlation, random coefficient distributions, and residual heteroscedasticity.

PubMed

Rights, Jason D; Sterba, Sonya K

2016-11-01

Multilevel data structures are common in the social sciences. Often, such nested data are analysed with multilevel models (MLMs) in which heterogeneity between clusters is modelled by continuously distributed random intercepts and/or slopes. Alternatively, the non-parametric multilevel regression mixture model (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this article is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of the NPMM as a non-parametric approximation of the MLM, with relaxed distributional assumptions. We define how seven standard and non-standard MLM specifications can be indirectly approximated by particular NPMM specifications. We provide formulas showing how the NPMM can serve as an approximation of the MLM in terms of intraclass correlation, random coefficient means and (co)variances, heteroscedasticity of residuals at level 1, and heteroscedasticity of residuals at level 2. Further, we discuss how these relationships can be useful in practice. The specific relationships are illustrated with simulated graphical demonstrations, and direct and indirect interpretations of NPMM classes are contrasted. We provide an R function to aid in implementing and visualizing an indirect interpretation of NPMM classes. An empirical example is presented and future directions are discussed. © 2016 The British Psychological Society.

Nonparametric Statistics Test Software Package.

DTIC Science & Technology

1983-09-01

statis- tics because of their acceptance in the academic world, the availability of computer support, and flexibility in model builling. Nonparametric...25 I1l,lCELL WRITE(NCF,12 ) IvE (I ,RCCT(I) 122 FORMAT(IlXt 3(H5 9 1) IF( IeLT *NCELL) WRITE (NOF1123 J PARTV(I1J 123 FORMAT( Xll----’,FIo.3J 25 CONT

Relationships between QT interval and heart rate variability at rest and the covariates in healthy young adults.

PubMed

Arai, Kaori; Nakagawa, Yui; Iwata, Toyoto; Horiguchi, Hyogo; Murata, Katsuyuki

2013-01-01

To clarify the links between ECG QT-related parameters and heart rate variability (HRV) and the covariates possibly distorting them, the averaged RR and QT intervals in a single lead ECG were measured for 64 male and 86 female subjects aged 18-26. The QT index, defined by Rautaharju et al., in the young adults was not significantly related to any HRV parameters nor heart rate, but the Bazett's corrected QT (QTc) interval was associated negatively with the parasympathetic activity and positively with heart rate. No significant differences in the QTc interval, QT index or heart rate were seen between the men and women, but they significantly differed between both sexes after adjustment for possible covariates such as age and body mass index (BMI). Significant sex differences in parasympathetic parameters of the HRV were unchanged before and after the adjustment, but significant differences observed in the unadjusted sympathetic parameters disappeared after adjusting for covariates. Age, BMI and body fat percentage also were significant covariates affecting these ECG parameters. Consequently, QT index, unaffected by heart rate and HRV parameters, appears to be a more useful indicator than the QTc interval. Instead, the QT index and HRV parameters are recommended to be simultaneously measured in epidemiological research because they are probably complementary in assessing autonomic nervous function. Also, these parameters should be analyzed in men and women separately. Copyright © 2012 Elsevier B.V. All rights reserved.

A comparison of methods for organ-weight data adjustment in chicks.

PubMed

Brown, D R; Southern, L L; Baker, D H

1985-02-01

An experiment was conducted with 168 Arbor Acre X Peterson unsexed, crossbred broiler chicks to compare methods of expressing organ-weight data and to assess changes in organ weights and physiological parameters as body weight (97 to 791 g) and age (5 to 26 days) increased. Actual wet weight of liver, heart, intestine, spleen, and pancreas and percent bone ash increased (P less than .01) as age and body weight increased. Tibia length-to-width ratio decreased (P less than .01) as age and body weight increased. Blood hemoglobin, hematocrit, and plasma protein were not affected (P greater than .1) by age or by body weight. Liver, heart, and intestinal weight decreased (P less than .01) and spleen weight increased (P less than .01) as body weight and age increased when these tissue weights were expressed as percent of body weight. Liver weight adjusted for body weight by covariance analysis, however, remained constant; adjusted heart and intestinal weights decreased (P less than .01), and adjusted spleen weights increased (P less than .01) with increasing age and body weight. The covariate, body weight, was not significant (P greater than .1) for pancreas weight, tibia length-to-width ratio, and percent bone ash. Except for spleen, adjustment by covariance analysis more effectively reduced variation due to body weight than did expression as percent of body weight.(ABSTRACT TRUNCATED AT 250 WORDS)

A class of covariate-dependent spatiotemporal covariance functions

PubMed Central

Reich, Brian J; Eidsvik, Jo; Guindani, Michele; Nail, Amy J; Schmidt, Alexandra M.

2014-01-01

In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in the correlation structure. Therefore, it has been of prolonged interest in the literature to provide flexible and effective ways to model non-stationarity in the spatial effects. Arguably, due to the local nature of the problem, we might envision that the correlation structure would be highly dependent on local characteristics of the domain of study, namely the latitude, longitude and altitude of the observation sites, as well as other locally defined covariate information. In this work, we provide a flexible and computationally feasible way for allowing the correlation structure of the underlying processes to depend on local covariate information. We discuss the properties of the induced covariance functions and discuss methods to assess its dependence on local covariate information by means of a simulation study and the analysis of data observed at ozone-monitoring stations in the Southeast United States. PMID:24772199

Nonparametric probability density estimation by optimization theoretic techniques

NASA Technical Reports Server (NTRS)

Scott, D. W.

1976-01-01

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

Kernel Equating Under the Non-Equivalent Groups With Covariates Design

PubMed Central

Bränberg, Kenny

2015-01-01

When equating two tests, the traditional approach is to use common test takers and/or common items. Here, the idea is to use variables correlated with the test scores (e.g., school grades and other test scores) as a substitute for common items in a non-equivalent groups with covariates (NEC) design. This is performed in the framework of kernel equating and with an extension of the method developed for post-stratification equating in the non-equivalent groups with anchor test design. Real data from a college admissions test were used to illustrate the use of the design. The equated scores from the NEC design were compared with equated scores from the equivalent group (EG) design, that is, equating with no covariates as well as with equated scores when a constructed anchor test was used. The results indicate that the NEC design can produce lower standard errors compared with an EG design. When covariates were used together with an anchor test, the smallest standard errors were obtained over a large range of test scores. The results obtained, that an EG design equating can be improved by adjusting for differences in test score distributions caused by differences in the distribution of covariates, are useful in practice because not all standardized tests have anchor tests. PMID:29881012

Kernel Equating Under the Non-Equivalent Groups With Covariates Design.

PubMed

Wiberg, Marie; Bränberg, Kenny

2015-07-01

When equating two tests, the traditional approach is to use common test takers and/or common items. Here, the idea is to use variables correlated with the test scores (e.g., school grades and other test scores) as a substitute for common items in a non-equivalent groups with covariates (NEC) design. This is performed in the framework of kernel equating and with an extension of the method developed for post-stratification equating in the non-equivalent groups with anchor test design. Real data from a college admissions test were used to illustrate the use of the design. The equated scores from the NEC design were compared with equated scores from the equivalent group (EG) design, that is, equating with no covariates as well as with equated scores when a constructed anchor test was used. The results indicate that the NEC design can produce lower standard errors compared with an EG design. When covariates were used together with an anchor test, the smallest standard errors were obtained over a large range of test scores. The results obtained, that an EG design equating can be improved by adjusting for differences in test score distributions caused by differences in the distribution of covariates, are useful in practice because not all standardized tests have anchor tests.

GRAVSAT/GEOPAUSE covariance analysis including geopotential aliasing

NASA Technical Reports Server (NTRS)

Koch, D. W.

1975-01-01

A conventional covariance analysis for the GRAVSAT/GEOPAUSE mission is described in which the uncertainties of approximately 200 parameters, including the geopotential coefficients to degree and order 12, are estimated over three different tracking intervals. The estimated orbital uncertainties for both GRAVSAT and GEOPAUSE reach levels more accurate than presently available. The adjusted measurement bias errors approach the mission goal. Survey errors in the low centimeter range are achieved after ten days of tracking. The ability of the mission to obtain accuracies of geopotential terms to (12, 12) one to two orders of magnitude superior to present accuracy levels is clearly shown. A unique feature of this report is that the aliasing structure of this (12, 12) field is examined. It is shown that uncertainties for unadjusted terms to (12, 12) still exert a degrading effect upon the adjusted error of an arbitrarily selected term of lower degree and order. Finally, the distribution of the aliasing from the unestimated uncertainty of a particular high degree and order geopotential term upon the errors of all remaining adjusted terms is listed in detail.

Robust covariance estimation of galaxy-galaxy weak lensing: validation and limitation of jackknife covariance

NASA Astrophysics Data System (ADS)

Shirasaki, Masato; Takada, Masahiro; Miyatake, Hironao; Takahashi, Ryuichi; Hamana, Takashi; Nishimichi, Takahiro; Murata, Ryoma

2017-09-01

We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations and their inherent halo catalogues. Using the mock catalogue to study the error covariance matrix of galaxy-galaxy weak lensing, we compare the full covariance with the 'jackknife' (JK) covariance, the method often used in the literature that estimates the covariance from the resamples of the data itself. We show that there exists the variation of JK covariance over realizations of mock lensing measurements, while the average JK covariance over mocks can give a reasonably accurate estimation of the true covariance up to separations comparable with the size of JK subregion. The scatter in JK covariances is found to be ∼10 per cent after we subtract the lensing measurement around random points. However, the JK method tends to underestimate the covariance at the larger separations, more increasingly for a survey with a higher number density of source galaxies. We apply our method to the Sloan Digital Sky Survey (SDSS) data, and show that the 48 mock SDSS catalogues nicely reproduce the signals and the JK covariance measured from the real data. We then argue that the use of the accurate covariance, compared to the JK covariance, allows us to use the lensing signals at large scales beyond a size of the JK subregion, which contains cleaner cosmological information in the linear regime.

Regionalizing nonparametric models of precipitation amounts on different temporal scales

NASA Astrophysics Data System (ADS)

Mosthaf, Tobias; Bárdossy, András

2017-05-01

Parametric distribution functions are commonly used to model precipitation amounts corresponding to different durations. The precipitation amounts themselves are crucial for stochastic rainfall generators and weather generators. Nonparametric kernel density estimates (KDEs) offer a more flexible way to model precipitation amounts. As already stated in their name, these models do not exhibit parameters that can be easily regionalized to run rainfall generators at ungauged locations as well as at gauged locations. To overcome this deficiency, we present a new interpolation scheme for nonparametric models and evaluate it for different temporal resolutions ranging from hourly to monthly. During the evaluation, the nonparametric methods are compared to commonly used parametric models like the two-parameter gamma and the mixed-exponential distribution. As water volume is considered to be an essential parameter for applications like flood modeling, a Lorenz-curve-based criterion is also introduced. To add value to the estimation of data at sub-daily resolutions, we incorporated the plentiful daily measurements in the interpolation scheme, and this idea was evaluated. The study region is the federal state of Baden-Württemberg in the southwest of Germany with more than 500 rain gauges. The validation results show that the newly proposed nonparametric interpolation scheme provides reasonable results and that the incorporation of daily values in the regionalization of sub-daily models is very beneficial.

Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization.

PubMed

Brier, Matthew R; Mitra, Anish; McCarthy, John E; Ances, Beau M; Snyder, Abraham Z

2015-11-01

Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a complicated covariance structure. Partial covariance assesses the unique variance shared between two brain regions excluding any widely shared variance, hence is appropriate for the analysis of multivariate fMRI datasets. However, calculation of partial covariance requires inversion of the covariance matrix, which, in most functional connectivity studies, is not invertible owing to rank deficiency. Here we apply Ledoit-Wolf shrinkage (L2 regularization) to invert the high dimensional BOLD covariance matrix. We investigate the network organization and brain-state dependence of partial covariance-based functional connectivity. Although RSNs are conventionally defined in terms of shared variance, removal of widely shared variance, surprisingly, improved the separation of RSNs in a spring embedded graphical model. This result suggests that pair-wise unique shared variance plays a heretofore unrecognized role in RSN covariance organization. In addition, application of partial correlation to fMRI data acquired in the eyes open vs. eyes closed states revealed focal changes in uniquely shared variance between the thalamus and visual cortices. This result suggests that partial correlation of resting state BOLD time series reflect functional processes in addition to structural connectivity. Copyright © 2015 Elsevier Inc. All rights reserved.

Partial covariance based functional connectivity computation using Ledoit-Wolf covariance regularization

PubMed Central

Brier, Matthew R.; Mitra, Anish; McCarthy, John E.; Ances, Beau M.; Snyder, Abraham Z.

2015-01-01

Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a complicated covariance structure. Partial covariance assesses the unique variance shared between two brain regions excluding any widely shared variance, hence is appropriate for the analysis of multivariate fMRI datasets. However, calculation of partial covariance requires inversion of the covariance matrix, which, in most functional connectivity studies, is not invertible owing to rank deficiency. Here we apply Ledoit-Wolf shrinkage (L2 regularization) to invert the high dimensional BOLD covariance matrix. We investigate the network organization and brain-state dependence of partial covariance-based functional connectivity. Although RSNs are conventionally defined in terms of shared variance, removal of widely shared variance, surprisingly, improved the separation of RSNs in a spring embedded graphical model. This result suggests that pair-wise unique shared variance plays a heretofore unrecognized role in RSN covariance organization. In addition, application of partial correlation to fMRI data acquired in the eyes open vs. eyes closed states revealed focal changes in uniquely shared variance between the thalamus and visual cortices. This result suggests that partial correlation of resting state BOLD time series reflect functional processes in addition to structural connectivity. PMID:26208872

A Hybrid Index for Characterizing Drought Based on a Nonparametric Kernel Estimator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Shengzhi; Huang, Qiang; Leng, Guoyong

This study develops a nonparametric multivariate drought index, namely, the Nonparametric Multivariate Standardized Drought Index (NMSDI), by considering the variations of both precipitation and streamflow. Building upon previous efforts in constructing Nonparametric Multivariate Drought Index, we use the nonparametric kernel estimator to derive the joint distribution of precipitation and streamflow, thus providing additional insights in drought index development. The proposed NMSDI are applied in the Wei River Basin (WRB), based on which the drought evolution characteristics are investigated. Results indicate: (1) generally, NMSDI captures the drought onset similar to Standardized Precipitation Index (SPI) and drought termination and persistence similar tomore » Standardized Streamflow Index (SSFI). The drought events identified by NMSDI match well with historical drought records in the WRB. The performances are also consistent with that by an existing Multivariate Standardized Drought Index (MSDI) at various timescales, confirming the validity of the newly constructed NMSDI in drought detections (2) An increasing risk of drought has been detected for the past decades, and will be persistent to a certain extent in future in most areas of the WRB; (3) the identified change points of annual NMSDI are mainly concentrated in the early 1970s and middle 1990s, coincident with extensive water use and soil reservation practices. This study highlights the nonparametric multivariable drought index, which can be used for drought detections and predictions efficiently and comprehensively.« less

Covariate-free and Covariate-dependent Reliability.

PubMed

Bentler, Peter M

2016-12-01

Classical test theory reliability coefficients are said to be population specific. Reliability generalization, a meta-analysis method, is the main procedure for evaluating the stability of reliability coefficients across populations. A new approach is developed to evaluate the degree of invariance of reliability coefficients to population characteristics. Factor or common variance of a reliability measure is partitioned into parts that are, and are not, influenced by control variables, resulting in a partition of reliability into a covariate-dependent and a covariate-free part. The approach can be implemented in a single sample and can be applied to a variety of reliability coefficients.

Nonparametric Simulation of Signal Transduction Networks with Semi-Synchronized Update

PubMed Central

Nassiri, Isar; Masoudi-Nejad, Ali; Jalili, Mahdi; Moeini, Ali

2012-01-01

Simulating signal transduction in cellular signaling networks provides predictions of network dynamics by quantifying the changes in concentration and activity-level of the individual proteins. Since numerical values of kinetic parameters might be difficult to obtain, it is imperative to develop non-parametric approaches that combine the connectivity of a network with the response of individual proteins to signals which travel through the network. The activity levels of signaling proteins computed through existing non-parametric modeling tools do not show significant correlations with the observed values in experimental results. In this work we developed a non-parametric computational framework to describe the profile of the evolving process and the time course of the proportion of active form of molecules in the signal transduction networks. The model is also capable of incorporating perturbations. The model was validated on four signaling networks showing that it can effectively uncover the activity levels and trends of response during signal transduction process. PMID:22737250

Nonparametric instrumental regression with non-convex constraints

NASA Astrophysics Data System (ADS)

Grasmair, M.; Scherzer, O.; Vanhems, A.

2013-03-01

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition.

Nonparametric triple collocation

USDA-ARS?s Scientific Manuscript database

Triple collocation derives variance-covariance relationships between three or more independent measurement sources and an indirectly observed truth variable in the case where the measurement operators are linear-Gaussian. We generalize that theory to arbitrary observation operators by deriving nonpa...

A Bayesian nonparametric method for prediction in EST analysis

PubMed Central

Lijoi, Antonio; Mena, Ramsés H; Prünster, Igor

2007-01-01

Background Expressed sequence tags (ESTs) analyses are a fundamental tool for gene identification in organisms. Given a preliminary EST sample from a certain library, several statistical prediction problems arise. In particular, it is of interest to estimate how many new genes can be detected in a future EST sample of given size and also to determine the gene discovery rate: these estimates represent the basis for deciding whether to proceed sequencing the library and, in case of a positive decision, a guideline for selecting the size of the new sample. Such information is also useful for establishing sequencing efficiency in experimental design and for measuring the degree of redundancy of an EST library. Results In this work we propose a Bayesian nonparametric approach for tackling statistical problems related to EST surveys. In particular, we provide estimates for: a) the coverage, defined as the proportion of unique genes in the library represented in the given sample of reads; b) the number of new unique genes to be observed in a future sample; c) the discovery rate of new genes as a function of the future sample size. The Bayesian nonparametric model we adopt conveys, in a statistically rigorous way, the available information into prediction. Our proposal has appealing properties over frequentist nonparametric methods, which become unstable when prediction is required for large future samples. EST libraries, previously studied with frequentist methods, are analyzed in detail. Conclusion The Bayesian nonparametric approach we undertake yields valuable tools for gene capture and prediction in EST libraries. The estimators we obtain do not feature the kind of drawbacks associated with frequentist estimators and are reliable for any size of the additional sample. PMID:17868445

Thirty Years of Nonparametric Item Response Theory.

ERIC Educational Resources Information Center

Molenaar, Ivo W.

2001-01-01

Discusses relationships between a mathematical measurement model and its real-world applications. Makes a distinction between large-scale data matrices commonly found in educational measurement and smaller matrices found in attitude and personality measurement. Also evaluates nonparametric methods for estimating item response functions and…

Earth Observing System Covariance Realism

NASA Technical Reports Server (NTRS)

Zaidi, Waqar H.; Hejduk, Matthew D.

2016-01-01

The purpose of covariance realism is to properly size a primary object's covariance in order to add validity to the calculation of the probability of collision. The covariance realism technique in this paper consists of three parts: collection/calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics. An empirical cumulative distribution function (ECDF) Goodness-of-Fit (GOF) method is employed to determine if a covariance is properly sized by comparing the empirical distribution of Mahalanobis distance calculations to the hypothesized parent 3-DoF chi-squared distribution. To realistically size a covariance for collision probability calculations, this study uses a state noise compensation algorithm that adds process noise to the definitive epoch covariance to account for uncertainty in the force model. Process noise is added until the GOF tests pass a group significance level threshold. The results of this study indicate that when outliers attributed to persistently high or extreme levels of solar activity are removed, the aforementioned covariance realism compensation method produces a tuned covariance with up to 80 to 90% of the covariance propagation timespan passing (against a 60% minimum passing threshold) the GOF tests-a quite satisfactory and useful result.

Corrected score estimation in the proportional hazards model with misclassified discrete covariates

PubMed Central

Zucker, David M.; Spiegelman, Donna

2013-01-01

SUMMARY We consider Cox proportional hazards regression when the covariate vector includes error-prone discrete covariates along with error-free covariates, which may be discrete or continuous. The misclassification in the discrete error-prone covariates is allowed to be of any specified form. Building on the work of Nakamura and his colleagues, we present a corrected score method for this setting. The method can handle all three major study designs (internal validation design, external validation design, and replicate measures design), both functional and structural error models, and time-dependent covariates satisfying a certain ‘localized error’ condition. We derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix. We present the results of a finite-sample simulation study under Weibull survival with a single binary covariate having known misclassification rates. The performance of the method described here was similar to that of related methods we have examined in previous works. Specifically, our new estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study. Our method generally performed well in these simulations. The new estimator has a broader range of applicability than many other estimators proposed in the literature, including those described in our own earlier work, in that it can handle time-dependent covariates with an arbitrary misclassification structure. We illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer. PMID:18219700

Using indirect covariance spectra to identify artifact responses in unsymmetrical indirect covariance calculated spectra.

PubMed

Martin, Gary E; Hilton, Bruce D; Blinov, Kirill A; Williams, Antony J

2008-02-01

Several groups of authors have reported studies in the areas of indirect and unsymmetrical indirect covariance NMR processing methods. Efforts have recently focused on the use of unsymmetrical indirect covariance processing methods to combine various discrete two-dimensional NMR spectra to afford the equivalent of the much less sensitive hyphenated 2D NMR experiments, for example indirect covariance (icv)-heteronuclear single quantum coherence (HSQC)-COSY and icv-HSQC-nuclear Overhauser effect spectroscopy (NOESY). Alternatively, unsymmetrical indirect covariance processing methods can be used to combine multiple heteronuclear 2D spectra to afford icv-13C-15N HSQC-HMBC correlation spectra. We now report the use of responses contained in indirect covariance processed HSQC spectra as a means for the identification of artifacts in both indirect covariance and unsymmetrical indirect covariance processed 2D NMR spectra. Copyright (c) 2007 John Wiley & Sons, Ltd.

A nonparametric stochastic method for generating daily climate-adjusted streamflows

NASA Astrophysics Data System (ADS)

Stagge, J. H.; Moglen, G. E.

2013-10-01

A daily stochastic streamflow generation model is presented, which successfully replicates statistics of the historical streamflow record and can produce climate-adjusted daily time series. A monthly climate model relates general circulation model (GCM)-scale climate indicators to discrete climate-streamflow states, which in turn control parameters in a daily streamflow generation model. Daily flow is generated by a two-state (increasing/decreasing) Markov chain, with rising limb increments randomly sampled from a Weibull distribution and the falling limb modeled as exponential recession. When applied to the Potomac River, a 38,000 km2 basin in the Mid-Atlantic United States, the model reproduces the daily, monthly, and annual distribution and dynamics of the historical streamflow record, including extreme low flows. This method can be used as part of water resources planning, vulnerability, and adaptation studies and offers the advantage of a parsimonious model, requiring only a sufficiently long historical streamflow record and large-scale climate data. Simulation of Potomac streamflows subject to the Special Report on Emissions Scenarios (SRES) A1b, A2, and B1 emission scenarios predict a slight increase in mean annual flows over the next century, with the majority of this increase occurring during the winter and early spring. Conversely, mean summer flows are projected to decrease due to climate change, caused by a shift to shorter, more sporadic rain events. Date of the minimum annual flow is projected to shift 2-5 days earlier by the 2070-2099 period.

Nonparametric analysis of Minnesota spruce and aspen tree data and LANDSAT data

NASA Technical Reports Server (NTRS)

Scott, D. W.; Jee, R.

1984-01-01

The application of nonparametric methods in data-intensive problems faced by NASA is described. The theoretical development of efficient multivariate density estimators and the novel use of color graphics workstations are reviewed. The use of nonparametric density estimates for data representation and for Bayesian classification are described and illustrated. Progress in building a data analysis system in a workstation environment is reviewed and preliminary runs presented.

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Nonparametric evaluation of birth cohort trends in disease rates.

PubMed

Tarone, R E; Chu, K C

2000-01-01

Although interpretation of age-period-cohort analyses is complicated by the non-identifiability of maximum likelihood estimates, changes in the slope of the birth-cohort effect curve are identifiable and have potential aetiologic significance. A nonparametric test for a change in the slope of the birth-cohort trend has been developed. The test is a generalisation of the sign test and is based on permutational distributions. A method for identifying interactions between age and calendar-period effects is also presented. The nonparametric method is shown to be powerful in detecting changes in the slope of the birth-cohort trend, although its power can be reduced considerably by calendar-period patterns of risk. The method identifies a previously unidentified decrease in the birth-cohort risk of lung-cancer mortality from 1912 to 1919, which appears to reflect a reduction in the initiation of smoking by young men at the beginning of the Great Depression (1930s). The method also detects an interaction between age and calendar period in leukemia mortality rates, reflecting the better response of children to chemotherapy. The proposed nonparametric method provides a data analytic approach, which is a useful adjunct to log-linear Poisson analysis of age-period-cohort models, either in the initial model building stage, or in the final interpretation stage.

Local kernel nonparametric discriminant analysis for adaptive extraction of complex structures

NASA Astrophysics Data System (ADS)

Li, Quanbao; Wei, Fajie; Zhou, Shenghan

2017-05-01

The linear discriminant analysis (LDA) is one of popular means for linear feature extraction. It usually performs well when the global data structure is consistent with the local data structure. Other frequently-used approaches of feature extraction usually require linear, independence, or large sample condition. However, in real world applications, these assumptions are not always satisfied or cannot be tested. In this paper, we introduce an adaptive method, local kernel nonparametric discriminant analysis (LKNDA), which integrates conventional discriminant analysis with nonparametric statistics. LKNDA is adept in identifying both complex nonlinear structures and the ad hoc rule. Six simulation cases demonstrate that LKNDA have both parametric and nonparametric algorithm advantages and higher classification accuracy. Quartic unilateral kernel function may provide better robustness of prediction than other functions. LKNDA gives an alternative solution for discriminant cases of complex nonlinear feature extraction or unknown feature extraction. At last, the application of LKNDA in the complex feature extraction of financial market activities is proposed.

Covariance mapping techniques

NASA Astrophysics Data System (ADS)

Frasinski, Leszek J.

2016-08-01

Recent technological advances in the generation of intense femtosecond pulses have made covariance mapping an attractive analytical technique. The laser pulses available are so intense that often thousands of ionisation and Coulomb explosion events will occur within each pulse. To understand the physics of these processes the photoelectrons and photoions need to be correlated, and covariance mapping is well suited for operating at the high counting rates of these laser sources. Partial covariance is particularly useful in experiments with x-ray free electron lasers, because it is capable of suppressing pulse fluctuation effects. A variety of covariance mapping methods is described: simple, partial (single- and multi-parameter), sliced, contingent and multi-dimensional. The relationship to coincidence techniques is discussed. Covariance mapping has been used in many areas of science and technology: inner-shell excitation and Auger decay, multiphoton and multielectron ionisation, time-of-flight and angle-resolved spectrometry, infrared spectroscopy, nuclear magnetic resonance imaging, stimulated Raman scattering, directional gamma ray sensing, welding diagnostics and brain connectivity studies (connectomics). This review gives practical advice for implementing the technique and interpreting the results, including its limitations and instrumental constraints. It also summarises recent theoretical studies, highlights unsolved problems and outlines a personal view on the most promising research directions.

Nonparametric estimation of plant density by the distance method

USGS Publications Warehouse

Patil, S.A.; Burnham, K.P.; Kovner, J.L.

1979-01-01

A relation between the plant density and the probability density function of the nearest neighbor distance (squared) from a random point is established under fairly broad conditions. Based upon this relationship, a nonparametric estimator for the plant density is developed and presented in terms of order statistics. Consistency and asymptotic normality of the estimator are discussed. An interval estimator for the density is obtained. The modifications of this estimator and its variance are given when the distribution is truncated. Simulation results are presented for regular, random and aggregated populations to illustrate the nonparametric estimator and its variance. A numerical example from field data is given. Merits and deficiencies of the estimator are discussed with regard to its robustness and variance.

Teaching Nonparametric Statistics Using Student Instrumental Values.

ERIC Educational Resources Information Center

Anderson, Jonathan W.; Diddams, Margaret

Nonparametric statistics are often difficult to teach in introduction to statistics courses because of the lack of real-world examples. This study demonstrated how teachers can use differences in the rankings and ratings of undergraduate and graduate values to discuss: (1) ipsative and normative scaling; (2) uses of the Mann-Whitney U-test; and…

A semi-nonparametric Poisson regression model for analyzing motor vehicle crash data.

PubMed

Ye, Xin; Wang, Ke; Zou, Yajie; Lord, Dominique

2018-01-01

This paper develops a semi-nonparametric Poisson regression model to analyze motor vehicle crash frequency data collected from rural multilane highway segments in California, US. Motor vehicle crash frequency on rural highway is a topic of interest in the area of transportation safety due to higher driving speeds and the resultant severity level. Unlike the traditional Negative Binomial (NB) model, the semi-nonparametric Poisson regression model can accommodate an unobserved heterogeneity following a highly flexible semi-nonparametric (SNP) distribution. Simulation experiments are conducted to demonstrate that the SNP distribution can well mimic a large family of distributions, including normal distributions, log-gamma distributions, bimodal and trimodal distributions. Empirical estimation results show that such flexibility offered by the SNP distribution can greatly improve model precision and the overall goodness-of-fit. The semi-nonparametric distribution can provide a better understanding of crash data structure through its ability to capture potential multimodality in the distribution of unobserved heterogeneity. When estimated coefficients in empirical models are compared, SNP and NB models are found to have a substantially different coefficient for the dummy variable indicating the lane width. The SNP model with better statistical performance suggests that the NB model overestimates the effect of lane width on crash frequency reduction by 83.1%.

A Bayesian Nonparametric Approach to Image Super-Resolution.

PubMed

Polatkan, Gungor; Zhou, Mingyuan; Carin, Lawrence; Blei, David; Daubechies, Ingrid

2015-02-01

Super-resolution methods form high-resolution images from low-resolution images. In this paper, we develop a new Bayesian nonparametric model for super-resolution. Our method uses a beta-Bernoulli process to learn a set of recurring visual patterns, called dictionary elements, from the data. Because it is nonparametric, the number of elements found is also determined from the data. We test the results on both benchmark and natural images, comparing with several other models from the research literature. We perform large-scale human evaluation experiments to assess the visual quality of the results. In a first implementation, we use Gibbs sampling to approximate the posterior. However, this algorithm is not feasible for large-scale data. To circumvent this, we then develop an online variational Bayes (VB) algorithm. This algorithm finds high quality dictionaries in a fraction of the time needed by the Gibbs sampler.

Methods and Issues for the Combined Use of Integral Experiments and Covariance Data: Results of a NEA International Collaborative Study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palmiotti, Giuseppe; Salvatores, Massimo

2014-04-01

The Working Party on International Nuclear Data Evaluation Cooperation (WPEC) of the Nuclear Science Committee under the Nuclear Energy Agency (NEA/OECD) established a Subgroup (called “Subgroup 33”) in 2009 on “Methods and issues for the combined use of integral experiments and covariance data.” The first stage was devoted to producing the description of different adjustment methodologies and assessing their merits. A detailed document related to this first stage has been issued. Nine leading organizations (often with a long and recognized expertise in the field) have contributed: ANL, CEA, INL, IPPE, JAEA, JSI, NRG, IRSN and ORNL. In the second stagemore » a practical benchmark exercise was defined in order to test the reliability of the nuclear data adjustment methodology. A comparison of the results obtained by the participants and major lessons learned in the exercise are discussed in the present paper that summarizes individual contributions which often include several original developments not reported separately. The paper provides the analysis of the most important results of the adjustment of the main nuclear data of 11 major isotopes in a 33-group energy structure. This benchmark exercise was based on a set of 20 well defined integral parameters from 7 fast assembly experiments. The exercise showed that using a common shared set of integral experiments but different starting evaluated libraries and/or different covariance matrices, there is a good convergence of trends for adjustments. Moreover, a significant reduction of the original uncertainties is often observed. Using the a–posteriori covariance data, there is a strong reduction of the uncertainties of integral parameters for reference reactor designs, mainly due to the new correlations in the a–posteriori covariance matrix. Furthermore, criteria have been proposed and applied to verify the consistency of differential and integral data used in the adjustment. Finally, recommendations

Nonparametric analysis of bivariate gap time with competing risks.

PubMed

Huang, Chiung-Yu; Wang, Chenguang; Wang, Mei-Cheng

2016-09-01

This article considers nonparametric methods for studying recurrent disease and death with competing risks. We first point out that comparisons based on the well-known cumulative incidence function can be confounded by different prevalence rates of the competing events, and that comparisons of the conditional distribution of the survival time given the failure event type are more relevant for investigating the prognosis of different patterns of recurrence disease. We then propose nonparametric estimators for the conditional cumulative incidence function as well as the conditional bivariate cumulative incidence function for the bivariate gap times, that is, the time to disease recurrence and the residual lifetime after recurrence. To quantify the association between the two gap times in the competing risks setting, a modified Kendall's tau statistic is proposed. The proposed estimators for the conditional bivariate cumulative incidence distribution and the association measure account for the induced dependent censoring for the second gap time. Uniform consistency and weak convergence of the proposed estimators are established. Hypothesis testing procedures for two-sample comparisons are discussed. Numerical simulation studies with practical sample sizes are conducted to evaluate the performance of the proposed nonparametric estimators and tests. An application to data from a pancreatic cancer study is presented to illustrate the methods developed in this article. © 2016, The International Biometric Society.

Balancing Score Adjusted Targeted Minimum Loss-based Estimation

PubMed Central

Lendle, Samuel David; Fireman, Bruce; van der Laan, Mark J.

2015-01-01

Adjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment-specific mean with the balancing score property that is additionally locally efficient and doubly robust. We investigate the new estimator’s performance relative to other estimators, including another TMLE, a propensity score matching estimator, an inverse probability of treatment weighted estimator, and a regression-based estimator in simulation studies. PMID:26561539

Computer codes for checking, plotting and processing of neutron cross-section covariance data and their application

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sartori, E.; Roussin, R.W.

This paper presents a brief review of computer codes concerned with checking, plotting, processing and using of covariances of neutron cross-section data. It concentrates on those available from the computer code information centers of the United States and the OECD/Nuclear Energy Agency. Emphasis will be placed also on codes using covariances for specific applications such as uncertainty analysis, data adjustment and data consistency analysis. Recent evaluations contain neutron cross section covariance information for all isotopes of major importance for technological applications of nuclear energy. It is therefore important that the available software tools needed for taking advantage of this informationmore » are widely known as hey permit the determination of better safety margins and allow the optimization of more economic, I designs of nuclear energy systems.« less

Kruskal-Wallis test: BASIC computer program to perform nonparametric one-way analysis of variance and multiple comparisons on ranks of several independent samples.

PubMed

Theodorsson-Norheim, E

1986-08-01

Multiple t tests at a fixed p level are frequently used to analyse biomedical data where analysis of variance followed by multiple comparisons or the adjustment of the p values according to Bonferroni would be more appropriate. The Kruskal-Wallis test is a nonparametric 'analysis of variance' which may be used to compare several independent samples. The present program is written in an elementary subset of BASIC and will perform Kruskal-Wallis test followed by multiple comparisons between the groups on practically any computer programmable in BASIC.

Covariance Bell inequalities

NASA Astrophysics Data System (ADS)

Pozsgay, Victor; Hirsch, Flavien; Branciard, Cyril; Brunner, Nicolas

2017-12-01

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities is their nonlinearity; this has nontrivial consequences for the derivation of their local bound, which is not reached by deterministic local correlations. For our simplest inequality, we derive analytically tight bounds for both local and quantum correlations. An interesting application of covariance Bell inequalities is that they can act as "shared randomness witnesses": specifically, the value of the Bell expression gives device-independent lower bounds on both the dimension and the entropy of the shared random variable in a local model.

Covariance Manipulation for Conjunction Assessment

NASA Technical Reports Server (NTRS)

Hejduk, M. D.

2016-01-01

The manipulation of space object covariances to try to provide additional or improved information to conjunction risk assessment is not an uncommon practice. Types of manipulation include fabricating a covariance when it is missing or unreliable to force the probability of collision (Pc) to a maximum value ('PcMax'), scaling a covariance to try to improve its realism or see the effect of covariance volatility on the calculated Pc, and constructing the equivalent of an epoch covariance at a convenient future point in the event ('covariance forecasting'). In bringing these methods to bear for Conjunction Assessment (CA) operations, however, some do not remain fully consistent with best practices for conducting risk management, some seem to be of relatively low utility, and some require additional information before they can contribute fully to risk analysis. This study describes some basic principles of modern risk management (following the Kaplan construct) and then examines the PcMax and covariance forecasting paradigms for alignment with these principles; it then further examines the expected utility of these methods in the modern CA framework. Both paradigms are found to be not without utility, but only in situations that are somewhat carefully circumscribed.

Towards a covariance matrix of CAB model parameters for H(H2O)

NASA Astrophysics Data System (ADS)

Scotta, Juan Pablo; Noguere, Gilles; Damian, José Ignacio Marquez

2017-09-01

Preliminary results on the uncertainties of hydrogen into light water thermal scattering law of the CAB model are presented. It was done through a coupling between the nuclear data code CONRAD and the molecular dynamic simulations code GROMACS. The Generalized Least Square method was used to adjust the model parameters on evaluated data and generate covariance matrices between the CAB model parameters.

Model-free quantification of dynamic PET data using nonparametric deconvolution

PubMed Central

Zanderigo, Francesca; Parsey, Ramin V; Todd Ogden, R

2015-01-01

Dynamic positron emission tomography (PET) data are usually quantified using compartment models (CMs) or derived graphical approaches. Often, however, CMs either do not properly describe the tracer kinetics, or are not identifiable, leading to nonphysiologic estimates of the tracer binding. The PET data are modeled as the convolution of the metabolite-corrected input function and the tracer impulse response function (IRF) in the tissue. Using nonparametric deconvolution methods, it is possible to obtain model-free estimates of the IRF, from which functionals related to tracer volume of distribution and binding may be computed, but this approach has rarely been applied in PET. Here, we apply nonparametric deconvolution using singular value decomposition to simulated and test–retest clinical PET data with four reversible tracers well characterized by CMs ([11C]CUMI-101, [11C]DASB, [11C]PE2I, and [11C]WAY-100635), and systematically compare reproducibility, reliability, and identifiability of various IRF-derived functionals with that of traditional CMs outcomes. Results show that nonparametric deconvolution, completely free of any model assumptions, allows for estimates of tracer volume of distribution and binding that are very close to the estimates obtained with CMs and, in some cases, show better test–retest performance than CMs outcomes. PMID:25873427

Testing and Estimating Shape-Constrained Nonparametric Density and Regression in the Presence of Measurement Error.

PubMed

Carroll, Raymond J; Delaigle, Aurore; Hall, Peter

2011-03-01

In many applications we can expect that, or are interested to know if, a density function or a regression curve satisfies some specific shape constraints. For example, when the explanatory variable, X, represents the value taken by a treatment or dosage, the conditional mean of the response, Y , is often anticipated to be a monotone function of X. Indeed, if this regression mean is not monotone (in the appropriate direction) then the medical or commercial value of the treatment is likely to be significantly curtailed, at least for values of X that lie beyond the point at which monotonicity fails. In the case of a density, common shape constraints include log-concavity and unimodality. If we can correctly guess the shape of a curve, then nonparametric estimators can be improved by taking this information into account. Addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint, and, if the conclusion of the test is positive, a technique for estimating the curve subject to the constraint. Nonparametric methodology for solving these problems already exists, but only in cases where the covariates are observed precisely. However in many problems, data can only be observed with measurement errors, and the methods employed in the error-free case typically do not carry over to this error context. In this paper we develop a novel approach to hypothesis testing and function estimation under shape constraints, which is valid in the context of measurement errors. Our method is based on tilting an estimator of the density or the regression mean until it satisfies the shape constraint, and we take as our test statistic the distance through which it is tilted. Bootstrap methods are used to calibrate the test. The constrained curve estimators that we develop are also based on tilting, and in that context our work has points of contact with methodology in the error-free case.

Traffic flow forecasting using approximate nearest neighbor nonparametric regression

DOT National Transportation Integrated Search

2000-12-01

The purpose of this research is to enhance nonparametric regression (NPR) for use in real-time systems by first reducing execution time using advanced data structures and imprecise computations and then developing a methodology for applying NPR. Due ...

A substantial and confusing variation exists in handling of baseline covariates in randomized controlled trials: a review of trials published in leading medical journals.

PubMed

Austin, Peter C; Manca, Andrea; Zwarenstein, Merrick; Juurlink, David N; Stanbrook, Matthew B

2010-02-01

Statisticians have criticized the use of significance testing to compare the distribution of baseline covariates between treatment groups in randomized controlled trials (RCTs). Furthermore, some have advocated for the use of regression adjustment to estimate the effect of treatment after adjusting for potential imbalances in prognostically important baseline covariates between treatment groups. We examined 114 RCTs published in the New England Journal of Medicine, the Journal of the American Medical Association, The Lancet, and the British Medical Journal between January 1, 2007 and June 30, 2007. Significance testing was used to compare baseline characteristics between treatment arms in 38% of the studies. The practice was very rare in British journals and more common in the U.S. journals. In 29% of the studies, the primary outcome was continuous, whereas in 65% of the studies, the primary outcome was either dichotomous or time-to-event in nature. Adjustment for baseline covariates was reported when estimating the treatment effect in 34% of the studies. Our findings suggest the need for greater editorial consistency across journals in the reporting of RCTs. Furthermore, there is a need for greater debate about the relative merits of unadjusted vs. adjusted estimates of treatment effect. Copyright 2010 Elsevier Inc. All rights reserved.

Nonparametric estimation of the multivariate survivor function: the multivariate Kaplan-Meier estimator.

PubMed

Prentice, Ross L; Zhao, Shanshan

2018-01-01

The Dabrowska (Ann Stat 16:1475-1489, 1988) product integral representation of the multivariate survivor function is extended, leading to a nonparametric survivor function estimator for an arbitrary number of failure time variates that has a simple recursive formula for its calculation. Empirical process methods are used to sketch proofs for this estimator's strong consistency and weak convergence properties. Summary measures of pairwise and higher-order dependencies are also defined and nonparametrically estimated. Simulation evaluation is given for the special case of three failure time variates.

Covariance of fluid-turbulence theory.

PubMed

Ariki, Taketo

2015-05-01

Covariance of physical quantities in fluid-turbulence theory and their governing equations under generalized coordinate transformation is discussed. It is shown that the velocity fluctuation and its governing law have a covariance under far wider group of coordinate transformation than that of conventional Euclidean invariance, and, as a natural consequence, various correlations and their governing laws are shown to be formulated in covariant manners under this wider transformation group. In addition, it is also shown that the covariance of the Reynolds stress is tightly connected to the objectivity of the mean flow.

Nonparametric functional data estimation applied to ozone data: prediction and extreme value analysis.

PubMed

Quintela-del-Río, Alejandro; Francisco-Fernández, Mario

2011-02-01

The study of extreme values and prediction of ozone data is an important topic of research when dealing with environmental problems. Classical extreme value theory is usually used in air-pollution studies. It consists in fitting a parametric generalised extreme value (GEV) distribution to a data set of extreme values, and using the estimated distribution to compute return levels and other quantities of interest. Here, we propose to estimate these values using nonparametric functional data methods. Functional data analysis is a relatively new statistical methodology that generally deals with data consisting of curves or multi-dimensional variables. In this paper, we use this technique, jointly with nonparametric curve estimation, to provide alternatives to the usual parametric statistical tools. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) in the UK. The results show that nonparametric estimators work satisfactorily, outperforming the behaviour of classical parametric estimators. Functional data analysis is also used to predict stratospheric ozone concentrations. We show an application, using the data set of mean monthly ozone concentrations in Arosa, Switzerland, and the results are compared with those obtained by classical time series (ARIMA) analysis. Copyright © 2010 Elsevier Ltd. All rights reserved.

A New Nonparametric Levene Test for Equal Variances

ERIC Educational Resources Information Center

Nordstokke, David W.; Zumbo, Bruno D.

2010-01-01

Tests of the equality of variances are sometimes used on their own to compare variability across groups of experimental or non-experimental conditions but they are most often used alongside other methods to support assumptions made about variances. A new nonparametric test of equality of variances is described and compared to current "gold…

A Unifying Framework for Teaching Nonparametric Statistical Tests

ERIC Educational Resources Information Center

Bargagliotti, Anna E.; Orrison, Michael E.

2014-01-01

Increased importance is being placed on statistics at both the K-12 and undergraduate level. Research divulging effective methods to teach specific statistical concepts is still widely sought after. In this paper, we focus on best practices for teaching topics in nonparametric statistics at the undergraduate level. To motivate the work, we…

Parametric and non-parametric modeling of short-term synaptic plasticity. Part I: computational study

PubMed Central

Marmarelis, Vasilis Z.; Berger, Theodore W.

2009-01-01

Parametric and non-parametric modeling methods are combined to study the short-term plasticity (STP) of synapses in the central nervous system (CNS). The nonlinear dynamics of STP are modeled by means: (1) previously proposed parametric models based on mechanistic hypotheses and/or specific dynamical processes, and (2) non-parametric models (in the form of Volterra kernels) that transforms the presynaptic signals into postsynaptic signals. In order to synergistically use the two approaches, we estimate the Volterra kernels of the parametric models of STP for four types of synapses using synthetic broadband input–output data. Results show that the non-parametric models accurately and efficiently replicate the input–output transformations of the parametric models. Volterra kernels provide a general and quantitative representation of the STP. PMID:18506609

Covariant Uniform Acceleration

NASA Astrophysics Data System (ADS)

Friedman, Yaakov; Scarr, Tzvi

2013-04-01

We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation , where F is the 3D force and p = m0γv is the 3D relativistic momentum. The standard 4D equation is only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. This solves a problem of Einstein and Planck. We compute explicit solutions for uniformly accelerated motion. The solutions are divided into four Lorentz-invariant types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We introduce the 4D velocity, an adaptation of Horwitz and Piron s notion of "off-shell." We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and

On the development of a semi-nonparametric generalized multinomial logit model for travel-related choices.

PubMed

Wang, Ke; Ye, Xin; Pendyala, Ram M; Zou, Yajie

2017-01-01

A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimation. The proposed method is applied to model commute mode choice among four alternatives (auto, transit, bicycle and walk) using travel behavior data from Argau, Switzerland. Comparisons between the multinomial logit model and the proposed semi-nonparametric model show that violations of the standard Gumbel distribution assumption lead to considerable inconsistency in parameter estimates and model inferences.

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected

PIA and REWIND: Two New Methodologies for Cross Section Adjustment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palmiotti, G.; Salvatores, M.

2017-02-01

This paper presents two new cross section adjustment methodologies intended for coping with the problem of compensations. The first one PIA, Progressive Incremental Adjustment, gives priority to the utilization of experiments of elemental type (those sensitive to a specific cross section), following a definite hierarchy on which type of experiment to use. Once the adjustment is performed, both the new adjusted data and the new covariance matrix are kept. The second methodology is called REWIND (Ranking Experiments by Weighting for Improved Nuclear Data). This new proposed approach tries to establish a methodology for ranking experiments by looking at the potentialmore » gain they can produce in an adjustment. Practical applications for different adjustments illustrate the results of the two methodologies against the current one and show the potential improvement for reducing uncertainties in target reactors.« less

Covariance Manipulation for Conjunction Assessment

NASA Technical Reports Server (NTRS)

Hejduk, M. D.

2016-01-01

Use of probability of collision (Pc) has brought sophistication to CA. Made possible by JSpOC precision catalogue because provides covariance. Has essentially replaced miss distance as basic CA parameter. Embrace of Pc has elevated methods to 'manipulate' covariance to enable/improve CA calculations. Two such methods to be examined here; compensation for absent or unreliable covariances through 'Maximum Pc' calculation constructs, projection (not propagation) of epoch covariances forward in time to try to enable better risk assessments. Two questions to be answered about each; situations to which such approaches are properly applicable, amount of utility that such methods offer.

Environmental Chemicals in Urine and Blood: Improving Methods for Creatinine and Lipid Adjustment.

PubMed

O'Brien, Katie M; Upson, Kristen; Cook, Nancy R; Weinberg, Clarice R

2016-02-01

Investigators measuring exposure biomarkers in urine typically adjust for creatinine to account for dilution-dependent sample variation in urine concentrations. Similarly, it is standard to adjust for serum lipids when measuring lipophilic chemicals in serum. However, there is controversy regarding the best approach, and existing methods may not effectively correct for measurement error. We compared adjustment methods, including novel approaches, using simulated case-control data. Using a directed acyclic graph framework, we defined six causal scenarios for epidemiologic studies of environmental chemicals measured in urine or serum. The scenarios include variables known to influence creatinine (e.g., age and hydration) or serum lipid levels (e.g., body mass index and recent fat intake). Over a range of true effect sizes, we analyzed each scenario using seven adjustment approaches and estimated the corresponding bias and confidence interval coverage across 1,000 simulated studies. For urinary biomarker measurements, our novel method, which incorporates both covariate-adjusted standardization and the inclusion of creatinine as a covariate in the regression model, had low bias and possessed 95% confidence interval coverage of nearly 95% for most simulated scenarios. For serum biomarker measurements, a similar approach involving standardization plus serum lipid level adjustment generally performed well. To control measurement error bias caused by variations in serum lipids or by urinary diluteness, we recommend improved methods for standardizing exposure concentrations across individuals.

Bayesian nonparametric dictionary learning for compressed sensing MRI.

PubMed

Huang, Yue; Paisley, John; Lin, Qin; Ding, Xinghao; Fu, Xueyang; Zhang, Xiao-Ping

2014-12-01

We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRIs) from highly undersampled k -space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov chain Monte Carlo for the Bayesian model, and use the alternating direction method of multipliers for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.

Sex hormones adjust "sex-specific" reactive and diurnal cortisol profiles.

PubMed

Juster, Robert-Paul; Raymond, Catherine; Desrochers, Alexandra Bisson; Bourdon, Olivier; Durand, Nadia; Wan, Nathalie; Pruessner, Jens C; Lupien, Sonia J

2016-01-01

Sex differences in stress hormone functions are presumed to depend on sex hormones. And yet, surprisingly few psychoneuroendocrine studies actually assess within-sex variations of testosterone, estradiol, and progesterone when investigating sex-specific activities of the hypothalamic-pituitary-adrenal axis. In this methodological study of 204 healthy adults (60 men), we assessed whether cortisol profiles would differ between the sexes when unadjusted or adjusted for basal sex hormones among both sexes. Reactive cortisol was sampled using 6 saliva samples measured every 10-min as part of the Trier Social Stress Test that generally activates cortisol among men more than women. Diurnal cortisol was sampled over two days at (1) awakening, (2) 30-min thereafter, (3) 1400 h, (4) 1600 h, and (5) bedtime. Sex hormones were collected at baseline before the psychosocial stressor and on two occasions during diurnal cortisol assessment. Repeated-measures analysis of covariance controlled for key covariates in analyses unadjusted or adjusted for sex hormones. Results revealed that men had higher reactive cortisol than women in unadjusted analysis, but this sex difference was attenuated when adjusting for sex hormones. While diurnal cortisol showed no sex differences in unadjusted models, adjusting for sex hormones revealed that women have higher morning cortisol. Correlations using area under the curve formulae revealed intriguing sex-specific associations with progesterone in men and testosterone in women that we propose have implications for social and affective neuroscience. In summary, our results reveal that adjusting for sex hormones alters "sex-specific" reactive and diurnal cortisol profiles. Copyright © 2015 Elsevier Ltd. All rights reserved.

Joint Entropy Minimization for Learning in Nonparametric Framework

DTIC Science & Technology

2006-06-09

Tibshirani, G. Sherlock , W. C. Chan, T. C. Greiner, D. D. Weisenburger, J. O. Armitage, R. Warnke, R. Levy, W. Wilson, M. R. Grever, J. C. Byrd, D. Botstein, P...Entropy Minimization for Learning in Nonparametric Framework 33 [11] D.L. Collins, A.P. Zijdenbos, J.G. Kollokian, N.J. Sled, C.J. Kabani, C.J. Holmes

On the development of a semi-nonparametric generalized multinomial logit model for travel-related choices

PubMed Central

Ye, Xin; Pendyala, Ram M.; Zou, Yajie

2017-01-01

A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimation. The proposed method is applied to model commute mode choice among four alternatives (auto, transit, bicycle and walk) using travel behavior data from Argau, Switzerland. Comparisons between the multinomial logit model and the proposed semi-nonparametric model show that violations of the standard Gumbel distribution assumption lead to considerable inconsistency in parameter estimates and model inferences. PMID:29073152

Comparing nonparametric Bayesian tree priors for clonal reconstruction of tumors.

PubMed

Deshwar, Amit G; Vembu, Shankar; Morris, Quaid

2015-01-01

Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the phylogeny and genotype of major subclonal lineages represented in the population of cancer cells. We also propose new split-merge updates tailored to the subclonal reconstruction problem that improve the mixing time of Markov chains. In comparisons with the tree-structured stick breaking prior used in PhyloSub, we demonstrate superior mixing and running time using the treeCRP with our new split-merge procedures. We also show that given the same number of samples, TSSB and treeCRP have similar ability to recover the subclonal structure of a tumor…

Two aspects of feedforward postural control: anticipatory postural adjustments and anticipatory synergy adjustments.

PubMed

Klous, Miriam; Mikulic, Pavle; Latash, Mark L

2011-05-01

We used the framework of the uncontrolled manifold hypothesis to explore the relations between anticipatory synergy adjustments (ASAs) and anticipatory postural adjustments (APAs) during feedforward control of vertical posture. ASAs represent a drop in the index of a multimuscle-mode synergy stabilizing the coordinate of the center of pressure in preparation to an action. ASAs reflect early changes of an index of covariation among variables reflecting muscle activation, whereas APAs reflect early changes in muscle activation levels averaged across trials. The assumed purpose of ASAs is to modify stability of performance variables, whereas the purpose of APAs is to change magnitudes of those variables. We hypothesized that ASAs would be seen before APAs and that this finding would be consistent with regard to the muscle-mode composition defined on the basis of different tasks and phases of action. Subjects performed a voluntary body sway task and a quick, bilateral shoulder flexion task under self-paced and reaction time conditions. Surface muscle activity of 12 leg and trunk muscles was analyzed to identify sets of 4 muscle modes for each task and for different phases within the shoulder flexion task. Variance components in the muscle-mode space and indexes of multimuscle-mode synergy stabilizing shift of the center of pressure were computed. ASAs were seen ∼ 100-150 ms prior to the task initiation, before APAs. The results were consistent with respect to different sets of muscle modes defined over the two tasks and different shoulder flexion phases. We conclude that the preparation for a self-triggered postural perturbation is associated with two types of anticipatory adjustments, ASAs and APAs. They reflect different feedforward processes within the hypothetical hierarchical control scheme, resulting in changes in patterns of covariation of elemental variables and in their patterns averaged across trials, respectively. The results show that synergies quantified

Enhanced brainstem and cortical evoked response amplitudes: single-trial covariance analysis.

PubMed

Galbraith, G C

2001-06-01

The purpose of the present study was to develop analytic procedures that improve the definition of sensory evoked response components. Such procedures could benefit all recordings but would especially benefit difficult recordings where many trials are contaminated by muscle and movement artifacts. First, cross-correlation and latency adjustment analyses were applied to the human brainstem frequency-following response and cortical auditory evoked response recorded on the same trials. Lagged cross-correlation functions were computed, for each of 17 subjects, between single-trial data and templates consisting of the sinusoid stimulus waveform for the brainstem response and the subject's own smoothed averaged evoked response P2 component for the cortical response. Trials were considered in the analysis only if the maximum correlation-squared (r2) exceeded .5 (negatively correlated trials were thus included). Identical correlation coefficients may be based on signals with quite different amplitudes, but it is possible to assess amplitude by the nonnormalized covariance function. Next, an algorithm is applied in which each trial with negative covariance is matched to a trial with similar, but positive, covariance and these matched-trial pairs are deleted. When an evoked response signal is present in the data, the majority of trials positively correlate with the template. Thus, a residual of positively correlated trials remains after matched covariance trials are deleted. When these residual trials are averaged, the resulting brainstem and cortical responses show greatly enhanced amplitudes. This result supports the utility of this analysis technique in clarifying and assessing evoked response signals.

On the Use of Nonparametric Item Characteristic Curve Estimation Techniques for Checking Parametric Model Fit

ERIC Educational Resources Information Center

Lee, Young-Sun; Wollack, James A.; Douglas, Jeffrey

2009-01-01

The purpose of this study was to assess the model fit of a 2PL through comparison with the nonparametric item characteristic curve (ICC) estimation procedures. Results indicate that three nonparametric procedures implemented produced ICCs that are similar to that of the 2PL for items simulated to fit the 2PL. However for misfitting items,…

Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes.

PubMed

Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D

2016-10-01

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. © The Author 2016. Published by Oxford University Press.

Nonparametric model validations for hidden Markov models with applications in financial econometrics.

PubMed

Zhao, Zhibiao

2011-06-01

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise.

Nonparametric model validations for hidden Markov models with applications in financial econometrics

PubMed Central

Zhao, Zhibiao

2011-01-01

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise. PMID:21750601

A comparative study of nonparametric methods for pattern recognition

NASA Technical Reports Server (NTRS)

Hahn, S. F.; Nelson, G. D.

1972-01-01

The applied research discussed in this report determines and compares the correct classification percentage of the nonparametric sign test, Wilcoxon's signed rank test, and K-class classifier with the performance of the Bayes classifier. The performance is determined for data which have Gaussian, Laplacian and Rayleigh probability density functions. The correct classification percentage is shown graphically for differences in modes and/or means of the probability density functions for four, eight and sixteen samples. The K-class classifier performed very well with respect to the other classifiers used. Since the K-class classifier is a nonparametric technique, it usually performed better than the Bayes classifier which assumes the data to be Gaussian even though it may not be. The K-class classifier has the advantage over the Bayes in that it works well with non-Gaussian data without having to determine the probability density function of the data. It should be noted that the data in this experiment was always unimodal.

Covariance Partition Priors: A Bayesian Approach to Simultaneous Covariance Estimation for Longitudinal Data.

PubMed

Gaskins, J T; Daniels, M J

2016-01-02

The estimation of the covariance matrix is a key concern in the analysis of longitudinal data. When data consists of multiple groups, it is often assumed the covariance matrices are either equal across groups or are completely distinct. We seek methodology to allow borrowing of strength across potentially similar groups to improve estimation. To that end, we introduce a covariance partition prior which proposes a partition of the groups at each measurement time. Groups in the same set of the partition share dependence parameters for the distribution of the current measurement given the preceding ones, and the sequence of partitions is modeled as a Markov chain to encourage similar structure at nearby measurement times. This approach additionally encourages a lower-dimensional structure of the covariance matrices by shrinking the parameters of the Cholesky decomposition toward zero. We demonstrate the performance of our model through two simulation studies and the analysis of data from a depression study. This article includes Supplementary Material available online.

Robust multivariate nonparametric tests for detection of two-sample location shift in clinical trials

PubMed Central

Jiang, Xuejun; Guo, Xu; Zhang, Ning; Wang, Bo

2018-01-01

This article presents and investigates performance of a series of robust multivariate nonparametric tests for detection of location shift between two multivariate samples in randomized controlled trials. The tests are built upon robust estimators of distribution locations (medians, Hodges-Lehmann estimators, and an extended U statistic) with both unscaled and scaled versions. The nonparametric tests are robust to outliers and do not assume that the two samples are drawn from multivariate normal distributions. Bootstrap and permutation approaches are introduced for determining the p-values of the proposed test statistics. Simulation studies are conducted and numerical results are reported to examine performance of the proposed statistical tests. The numerical results demonstrate that the robust multivariate nonparametric tests constructed from the Hodges-Lehmann estimators are more efficient than those based on medians and the extended U statistic. The permutation approach can provide a more stringent control of Type I error and is generally more powerful than the bootstrap procedure. The proposed robust nonparametric tests are applied to detect multivariate distributional difference between the intervention and control groups in the Thai Healthy Choices study and examine the intervention effect of a four-session motivational interviewing-based intervention developed in the study to reduce risk behaviors among youth living with HIV. PMID:29672555

Nonparametric method for failures diagnosis in the actuating subsystem of aircraft control system

NASA Astrophysics Data System (ADS)

Terentev, M. N.; Karpenko, S. S.; Zybin, E. Yu; Kosyanchuk, V. V.

2018-02-01

In this paper we design a nonparametric method for failures diagnosis in the aircraft control system that uses the measurements of the control signals and the aircraft states only. It doesn’t require a priori information of the aircraft model parameters, training or statistical calculations, and is based on analytical nonparametric one-step-ahead state prediction approach. This makes it possible to predict the behavior of unidentified and failure dynamic systems, to weaken the requirements to control signals, and to reduce the diagnostic time and problem complexity.

Parametric vs. non-parametric statistics of low resolution electromagnetic tomography (LORETA).

PubMed

Thatcher, R W; North, D; Biver, C

2005-01-01

This study compared the relative statistical sensitivity of non-parametric and parametric statistics of 3-dimensional current sources as estimated by the EEG inverse solution Low Resolution Electromagnetic Tomography (LORETA). One would expect approximately 5% false positives (classification of a normal as abnormal) at the P < .025 level of probability (two tailed test) and approximately 1% false positives at the P < .005 level. EEG digital samples (2 second intervals sampled 128 Hz, 1 to 2 minutes eyes closed) from 43 normal adult subjects were imported into the Key Institute's LORETA program. We then used the Key Institute's cross-spectrum and the Key Institute's LORETA output files (*.lor) as the 2,394 gray matter pixel representation of 3-dimensional currents at different frequencies. The mean and standard deviation *.lor files were computed for each of the 2,394 gray matter pixels for each of the 43 subjects. Tests of Gaussianity and different transforms were computed in order to best approximate a normal distribution for each frequency and gray matter pixel. The relative sensitivity of parametric vs. non-parametric statistics were compared using a "leave-one-out" cross validation method in which individual normal subjects were withdrawn and then statistically classified as being either normal or abnormal based on the remaining subjects. Log10 transforms approximated Gaussian distribution in the range of 95% to 99% accuracy. Parametric Z score tests at P < .05 cross-validation demonstrated an average misclassification rate of approximately 4.25%, and range over the 2,394 gray matter pixels was 27.66% to 0.11%. At P < .01 parametric Z score cross-validation false positives were 0.26% and ranged from 6.65% to 0% false positives. The non-parametric Key Institute's t-max statistic at P < .05 had an average misclassification error rate of 7.64% and ranged from 43.37% to 0.04% false positives. The nonparametric t-max at P < .01 had an average misclassification rate

Reliability of Test Scores in Nonparametric Item Response Theory.

ERIC Educational Resources Information Center

Sijtsma, Klaas; Molenaar, Ivo W.

1987-01-01

Three methods for estimating reliability are studied within the context of nonparametric item response theory. Two were proposed originally by Mokken and a third is developed in this paper. Using a Monte Carlo strategy, these three estimation methods are compared with four "classical" lower bounds to reliability. (Author/JAZ)

Design of adaptive control systems by means of self-adjusting transversal filters

NASA Technical Reports Server (NTRS)

Merhav, S. J.

1986-01-01

The design of closed-loop adaptive control systems based on nonparametric identification was addressed. Implementation is by self-adjusting Least Mean Square (LMS) transversal filters. The design concept is Model Reference Adaptive Control (MRAC). Major issues are to preserve the linearity of the error equations of each LMS filter, and to prevent estimation bias that is due to process or measurement noise, thus providing necessary conditions for the convergence and stability of the control system. The controlled element is assumed to be asymptotically stable and minimum phase. Because of the nonparametric Finite Impulse Response (FIR) estimates provided by the LMS filters, a-priori information on the plant model is needed only in broad terms. Following a survey of control system configurations and filter design considerations, system implementation is shown here in Single Input Single Output (SISO) format which is readily extendable to multivariable forms. In extensive computer simulation studies the controlled element is represented by a second-order system with widely varying damping, natural frequency, and relative degree.

Covariant diagrams for one-loop matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Zhengkang

Here, we present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We also show how such derivation canmore » be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.« less

Covariant diagrams for one-loop matching

DOE PAGES

Zhang, Zhengkang

2017-05-30

Here, we present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We also show how such derivation canmore » be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.« less

An entropy-based nonparametric test for the validation of surrogate endpoints.

PubMed

Miao, Xiaopeng; Wang, Yong-Cheng; Gangopadhyay, Ashis

2012-06-30

We present a nonparametric test to validate surrogate endpoints based on measure of divergence and random permutation. This test is a proposal to directly verify the Prentice statistical definition of surrogacy. The test does not impose distributional assumptions on the endpoints, and it is robust to model misspecification. Our simulation study shows that the proposed nonparametric test outperforms the practical test of the Prentice criterion in terms of both robustness of size and power. We also evaluate the performance of three leading methods that attempt to quantify the effect of surrogate endpoints. The proposed method is applied to validate magnetic resonance imaging lesions as the surrogate endpoint for clinical relapses in a multiple sclerosis trial. Copyright © 2012 John Wiley & Sons, Ltd.

Construction of Covariance Functions with Variable Length Fields

NASA Technical Reports Server (NTRS)

Gaspari, Gregory; Cohn, Stephen E.; Guo, Jing; Pawson, Steven

2005-01-01

This article focuses on construction, directly in physical space, of three-dimensional covariance functions parametrized by a tunable length field, and on an application of this theory to reproduce the Quasi-Biennial Oscillation (QBO) in the Goddard Earth Observing System, Version 4 (GEOS-4) data assimilation system. These Covariance models are referred to as multi-level or nonseparable, to associate them with the application where a multi-level covariance with a large troposphere to stratosphere length field gradient is used to reproduce the QBO from sparse radiosonde observations in the tropical lower stratosphere. The multi-level covariance functions extend well-known single level covariance functions depending only on a length scale. Generalizations of the first- and third-order autoregressive covariances in three dimensions are given, providing multi-level covariances with zero and three derivatives at zero separation, respectively. Multi-level piecewise rational covariances with two continuous derivatives at zero separation are also provided. Multi-level powerlaw covariances are constructed with continuous derivatives of all orders. Additional multi-level covariance functions are constructed using the Schur product of single and multi-level covariance functions. A multi-level powerlaw covariance used to reproduce the QBO in GEOS-4 is described along with details of the assimilation experiments. The new covariance model is shown to represent the vertical wind shear associated with the QBO much more effectively than in the baseline GEOS-4 system.

Analysis of covariance as a remedy for demographic mismatch of research subject groups: some sobering simulations.

PubMed

Adams, K M; Brown, G G; Grant, I

1985-08-01

Analysis of Covariance (ANCOVA) is often used in neuropsychological studies to effect ex-post-facto adjustment of performance variables amongst groups of subjects mismatched on some relevant demographic variable. This paper reviews some of the statistical assumptions underlying this usage. In an attempt to illustrate the complexities of this statistical technique, three sham studies using actual patient data are presented. These staged simulations have varying relationships between group test performance differences and levels of covariate discrepancy. The results were robust and consistent in their nature, and were held to support the wisdom of previous cautions by statisticians concerning the employment of ANCOVA to justify comparisons between incomparable groups. ANCOVA should not be used in neuropsychological research to equate groups unequal on variables such as age and education or to exert statistical control whose objective is to eliminate consideration of the covariate as an explanation for results. Finally, the report advocates by example the use of simulation to further our understanding of neuropsychological variables.

Three Classes of Nonparametric Differential Step Functioning Effect Estimators

ERIC Educational Resources Information Center

Penfield, Randall D.

2008-01-01

The examination of measurement invariance in polytomous items is complicated by the possibility that the magnitude and sign of lack of invariance may vary across the steps underlying the set of polytomous response options, a concept referred to as differential step functioning (DSF). This article describes three classes of nonparametric DSF effect…

Control Systems with Normalized and Covariance Adaptation by Optimal Control Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T. (Inventor); Burken, John J. (Inventor); Hanson, Curtis E. (Inventor)

2016-01-01

Disclosed is a novel adaptive control method and system called optimal control modification with normalization and covariance adjustment. The invention addresses specifically to current challenges with adaptive control in these areas: 1) persistent excitation, 2) complex nonlinear input-output mapping, 3) large inputs and persistent learning, and 4) the lack of stability analysis tools for certification. The invention has been subject to many simulations and flight testing. The results substantiate the effectiveness of the invention and demonstrate the technical feasibility for use in modern aircraft flight control systems.

Nonparametric Regression and the Parametric Bootstrap for Local Dependence Assessment.

ERIC Educational Resources Information Center

Habing, Brian

2001-01-01

Discusses ideas underlying nonparametric regression and the parametric bootstrap with an overview of their application to item response theory and the assessment of local dependence. Illustrates the use of the method in assessing local dependence that varies with examinee trait levels. (SLD)

Nonparametric weighted stochastic block models

NASA Astrophysics Data System (ADS)

Peixoto, Tiago P.

2018-01-01

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the model, which are instead inferred from data. We give a comprehensive treatment of different kinds of edge weights (i.e., continuous or discrete, signed or unsigned, bounded or unbounded), as well as arbitrary weight transformations, and describe an unsupervised model selection approach to choose the best network description. We illustrate the application of our method to a variety of empirical weighted networks, such as global migrations, voting patterns in congress, and neural connections in the human brain.

A Nonparametric K-Sample Test for Equality of Slopes.

ERIC Educational Resources Information Center

Penfield, Douglas A.; Koffler, Stephen L.

1986-01-01

The development of a nonparametric K-sample test for equality of slopes using Puri's generalized L statistic is presented. The test is recommended when the assumptions underlying the parametric model are violated. This procedure replaces original data with either ranks (for data with heavy tails) or normal scores (for data with light tails).…

On-line estimation of error covariance parameters for atmospheric data assimilation

NASA Technical Reports Server (NTRS)

Dee, Dick P.

1995-01-01

A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including

Covariance descriptor fusion for target detection

NASA Astrophysics Data System (ADS)

Cukur, Huseyin; Binol, Hamidullah; Bal, Abdullah; Yavuz, Fatih

2016-05-01

Target detection is one of the most important topics for military or civilian applications. In order to address such detection tasks, hyperspectral imaging sensors provide useful images data containing both spatial and spectral information. Target detection has various challenging scenarios for hyperspectral images. To overcome these challenges, covariance descriptor presents many advantages. Detection capability of the conventional covariance descriptor technique can be improved by fusion methods. In this paper, hyperspectral bands are clustered according to inter-bands correlation. Target detection is then realized by fusion of covariance descriptor results based on the band clusters. The proposed combination technique is denoted Covariance Descriptor Fusion (CDF). The efficiency of the CDF is evaluated by applying to hyperspectral imagery to detect man-made objects. The obtained results show that the CDF presents better performance than the conventional covariance descriptor.

Generalized Linear Covariance Analysis

NASA Technical Reports Server (NTRS)

Carpenter, James R.; Markley, F. Landis

2014-01-01

This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

Adjoints and Low-rank Covariance Representation

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.

2000-01-01

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Environmental Chemicals in Urine and Blood: Improving Methods for Creatinine and Lipid Adjustment

PubMed Central

O’Brien, Katie M.; Upson, Kristen; Cook, Nancy R.; Weinberg, Clarice R.

2015-01-01

Background Investigators measuring exposure biomarkers in urine typically adjust for creatinine to account for dilution-dependent sample variation in urine concentrations. Similarly, it is standard to adjust for serum lipids when measuring lipophilic chemicals in serum. However, there is controversy regarding the best approach, and existing methods may not effectively correct for measurement error. Objectives We compared adjustment methods, including novel approaches, using simulated case–control data. Methods Using a directed acyclic graph framework, we defined six causal scenarios for epidemiologic studies of environmental chemicals measured in urine or serum. The scenarios include variables known to influence creatinine (e.g., age and hydration) or serum lipid levels (e.g., body mass index and recent fat intake). Over a range of true effect sizes, we analyzed each scenario using seven adjustment approaches and estimated the corresponding bias and confidence interval coverage across 1,000 simulated studies. Results For urinary biomarker measurements, our novel method, which incorporates both covariate-adjusted standardization and the inclusion of creatinine as a covariate in the regression model, had low bias and possessed 95% confidence interval coverage of nearly 95% for most simulated scenarios. For serum biomarker measurements, a similar approach involving standardization plus serum lipid level adjustment generally performed well. Conclusions To control measurement error bias caused by variations in serum lipids or by urinary diluteness, we recommend improved methods for standardizing exposure concentrations across individuals. Citation O’Brien KM, Upson K, Cook NR, Weinberg CR. 2016. Environmental chemicals in urine and blood: improving methods for creatinine and lipid adjustment. Environ Health Perspect 124:220–227; http://dx.doi.org/10.1289/ehp.1509693 PMID:26219104

Computation of transform domain covariance matrices

NASA Technical Reports Server (NTRS)

Fino, B. J.; Algazi, V. R.

1975-01-01

It is often of interest in applications to compute the covariance matrix of a random process transformed by a fast unitary transform. Here, the recursive definition of fast unitary transforms is used to derive recursive relations for the covariance matrices of the transformed process. These relations lead to fast methods of computation of covariance matrices and to substantial reductions of the number of arithmetic operations required.

Stochastic Earthquake Rupture Modeling Using Nonparametric Co-Regionalization

NASA Astrophysics Data System (ADS)

Lee, Kyungbook; Song, Seok Goo

2017-09-01

Accurate predictions of the intensity and variability of ground motions are essential in simulation-based seismic hazard assessment. Advanced simulation-based ground motion prediction methods have been proposed to complement the empirical approach, which suffers from the lack of observed ground motion data, especially in the near-source region for large events. It is important to quantify the variability of the earthquake rupture process for future events and to produce a number of rupture scenario models to capture the variability in simulation-based ground motion predictions. In this study, we improved the previously developed stochastic earthquake rupture modeling method by applying the nonparametric co-regionalization, which was proposed in geostatistics, to the correlation models estimated from dynamically derived earthquake rupture models. The nonparametric approach adopted in this study is computationally efficient and, therefore, enables us to simulate numerous rupture scenarios, including large events ( M > 7.0). It also gives us an opportunity to check the shape of true input correlation models in stochastic modeling after being deformed for permissibility. We expect that this type of modeling will improve our ability to simulate a wide range of rupture scenario models and thereby predict ground motions and perform seismic hazard assessment more accurately.

Co-variation of tests commonly used in stroke rehabilitation.

PubMed

Langhammer, Birgitta; Stanghelle, Johan Kvalvik

2006-12-01

The aim of the present study was to analyse the co-variation of different tests commonly used in stroke rehabilitation, and specifically used in a recent randomized, controlled study of two different physiotherapy models in stroke rehabilitation. Correlations of the performed tests and recordings from previous work were studied. The test results from three-month, one-year and four-year follow-up were analysed in an SPSS Version 11 statistical package with Pearson and Spearman correlations. There was an expected high correlation between the motor function tests, both based on partial and total scores. The correlations between Nottingham Health Profile Part 1 and Motor Assessment Scale (MAS), Sødring Motor Evaluation Scale (SMES), the Berg Balance Scale (BBS) and Barthel Activities of Daily Living (ADL) index were low for all items except physical condition. The correlations between registered living conditions, assistive devices, recurrent stroke, motor function (MAS, SMES), ADL (Barthel ADL index) and balance (BBS) were high. The same variables showed weak or poor correlation to the Nottingham Health Profile (NHP). The co-variations of motor function tests and functional tests were high, but the co-variations of motor, functional and self-reported life-quality tests were poor. The patients rated themselves on a higher functional level in the self-reported tests than was observed objectively in the performance-based tests. A possible reason for this is that the patients may have been unaware they modified their performance to adjust for physical decline, and consequently overestimate their physical condition. This result underlines the importance of both performance-based and self-reported tests as complementary tools in a rehabilitation process.

Isavuconazole Population Pharmacokinetic Analysis Using Nonparametric Estimation in Patients with Invasive Fungal Disease (Results from the VITAL Study)

PubMed Central

Kovanda, Laura L.; Desai, Amit V.; Lu, Qiaoyang; Townsend, Robert W.; Akhtar, Shahzad; Bonate, Peter

2016-01-01

Isavuconazonium sulfate (Cresemba; Astellas Pharma Inc.), a water-soluble prodrug of the triazole antifungal agent isavuconazole, is available for the treatment of invasive aspergillosis (IA) and invasive mucormycosis. A population pharmacokinetic (PPK) model was constructed using nonparametric estimation to compare the pharmacokinetic (PK) behaviors of isavuconazole in patients treated in the phase 3 VITAL open-label clinical trial, which evaluated the efficacy and safety of the drug for treatment of renally impaired IA patients and patients with invasive fungal disease (IFD) caused by emerging molds, yeasts, and dimorphic fungi. Covariates examined were body mass index (BMI), weight, race, impact of estimated glomerular filtration rate (eGFR) on clearance (CL), and impact of weight on volume. PK parameters were compared based on IFD type and other patient characteristics. Simulations were performed to describe the MICs covered by the clinical dosing regimen. Concentrations (n = 458) from 136 patients were used to construct a 2-compartment model (first-order absorption compartment and central compartment). Weight-related covariates affected clearance, but eGFR did not. PK parameters and intersubject variability of CL were similar across different IFD groups and populations. Target attainment analyses demonstrated that the clinical dosing regimen would be sufficient for total drug area under the concentration-time curve (AUC)/MIC targets ranging from 50.5 for Aspergillus spp. (up to the CLSI MIC of 0.5 mg/liter) to 270 and 5,053 for Candida albicans (up to MICs of 0.125 and 0.004 mg/liter, respectively) and 312 for non-albicans Candida spp. (up to a MIC of 0.125 mg/liter). The estimations for Candida spp. were exploratory considering that no patients with Candida infections were included in the current analyses. (The VITAL trial is registered at ClinicalTrials.gov under number NCT00634049.) PMID:27185799

Relative-Error-Covariance Algorithms

NASA Technical Reports Server (NTRS)

Bierman, Gerald J.; Wolff, Peter J.

1991-01-01

Two algorithms compute error covariance of difference between optimal estimates, based on data acquired during overlapping or disjoint intervals, of state of discrete linear system. Provides quantitative measure of mutual consistency or inconsistency of estimates of states. Relative-error-covariance concept applied, to determine degree of correlation between trajectories calculated from two overlapping sets of measurements and construct real-time test of consistency of state estimates based upon recently acquired data.

Experiment Design for Nonparametric Models Based On Minimizing Bayes Risk: Application to Voriconazole1

PubMed Central

Bayard, David S.; Neely, Michael

2016-01-01

An experimental design approach is presented for individualized therapy in the special case where the prior information is specified by a nonparametric (NP) population model. Here, a nonparametric model refers to a discrete probability model characterized by a finite set of support points and their associated weights. An important question arises as to how to best design experiments for this type of model. Many experimental design methods are based on Fisher Information or other approaches originally developed for parametric models. While such approaches have been used with some success across various applications, it is interesting to note that they largely fail to address the fundamentally discrete nature of the nonparametric model. Specifically, the problem of identifying an individual from a nonparametric prior is more naturally treated as a problem of classification, i.e., to find a support point that best matches the patient’s behavior. This paper studies the discrete nature of the NP experiment design problem from a classification point of view. Several new insights are provided including the use of Bayes Risk as an information measure, and new alternative methods for experiment design. One particular method, denoted as MMopt (Multiple-Model Optimal), will be examined in detail and shown to require minimal computation while having distinct advantages compared to existing approaches. Several simulated examples, including a case study involving oral voriconazole in children, are given to demonstrate the usefulness of MMopt in pharmacokinetics applications. PMID:27909942

Nonparametric Bayesian models through probit stick-breaking processes

PubMed Central

Rodríguez, Abel; Dunson, David B.

2013-01-01

We describe a novel class of Bayesian nonparametric priors based on stick-breaking constructions where the weights of the process are constructed as probit transformations of normal random variables. We show that these priors are extremely flexible, allowing us to generate a great variety of models while preserving computational simplicity. Particular emphasis is placed on the construction of rich temporal and spatial processes, which are applied to two problems in finance and ecology. PMID:24358072

Nonparametric Bayesian models through probit stick-breaking processes.

PubMed

Rodríguez, Abel; Dunson, David B

2011-03-01

We describe a novel class of Bayesian nonparametric priors based on stick-breaking constructions where the weights of the process are constructed as probit transformations of normal random variables. We show that these priors are extremely flexible, allowing us to generate a great variety of models while preserving computational simplicity. Particular emphasis is placed on the construction of rich temporal and spatial processes, which are applied to two problems in finance and ecology.

Covariate analysis of bivariate survival data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bennett, L.E.

1992-01-01

The methods developed are used to analyze the effects of covariates on bivariate survival data when censoring and ties are present. The proposed method provides models for bivariate survival data that include differential covariate effects and censored observations. The proposed models are based on an extension of the univariate Buckley-James estimators which replace censored data points by their expected values, conditional on the censoring time and the covariates. For the bivariate situation, it is necessary to determine the expectation of the failure times for one component conditional on the failure or censoring time of the other component. Two different methodsmore » have been developed to estimate these expectations. In the semiparametric approach these expectations are determined from a modification of Burke's estimate of the bivariate empirical survival function. In the parametric approach censored data points are also replaced by their conditional expected values where the expected values are determined from a specified parametric distribution. The model estimation will be based on the revised data set, comprised of uncensored components and expected values for the censored components. The variance-covariance matrix for the estimated covariate parameters has also been derived for both the semiparametric and parametric methods. Data from the Demographic and Health Survey was analyzed by these methods. The two outcome variables are post-partum amenorrhea and breastfeeding; education and parity were used as the covariates. Both the covariate parameter estimates and the variance-covariance estimates for the semiparametric and parametric models will be compared. In addition, a multivariate test statistic was used in the semiparametric model to examine contrasts. The significance of the statistic was determined from a bootstrap distribution of the test statistic.« less

A Simulation Comparison of Parametric and Nonparametric Dimensionality Detection Procedures

ERIC Educational Resources Information Center

Mroch, Andrew A.; Bolt, Daniel M.

2006-01-01

Recently, nonparametric methods have been proposed that provide a dimensionally based description of test structure for tests with dichotomous items. Because such methods are based on different notions of dimensionality than are assumed when using a psychometric model, it remains unclear whether these procedures might lead to a different…

Measuring Youth Development: A Nonparametric Cross-Country "Youth Welfare Index"

ERIC Educational Resources Information Center

Chaaban, Jad M.

2009-01-01

This paper develops an empirical methodology for the construction of a synthetic multi-dimensional cross-country comparison of the performance of governments around the world in improving the livelihood of their younger population. The devised "Youth Welfare Index" is based on the nonparametric Data Envelopment Analysis (DEA) methodology and…

Bayesian Nonparametric Inference – Why and How

PubMed Central

Müller, Peter; Mitra, Riten

2013-01-01

We review inference under models with nonparametric Bayesian (BNP) priors. The discussion follows a set of examples for some common inference problems. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions. While we focus on arguing for the need for the flexibility of BNP models, we also review some of the more commonly used BNP models, thus hopefully answering a bit of both questions, why and how to use BNP. PMID:24368932

Lorentz covariance of loop quantum gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rovelli, Carlo; Speziale, Simone

2011-05-15

The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the projected spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleulermore » formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are precisely in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.« less

Assessment of water quality trends in the Minnesota River using non-parametric and parametric methods

USGS Publications Warehouse

Johnson, H.O.; Gupta, S.C.; Vecchia, A.V.; Zvomuya, F.

2009-01-01

Excessive loading of sediment and nutrients to rivers is a major problem in many parts of the United States. In this study, we tested the non-parametric Seasonal Kendall (SEAKEN) trend model and the parametric USGS Quality of Water trend program (QWTREND) to quantify trends in water quality of the Minnesota River at Fort Snelling from 1976 to 2003. Both methods indicated decreasing trends in flow-adjusted concentrations of total suspended solids (TSS), total phosphorus (TP), and orthophosphorus (OP) and a generally increasing trend in flow-adjusted nitrate plus nitrite-nitrogen (NO3-N) concentration. The SEAKEN results were strongly influenced by the length of the record as well as extreme years (dry or wet) earlier in the record. The QWTREND results, though influenced somewhat by the same factors, were more stable. The magnitudes of trends between the two methods were somewhat different and appeared to be associated with conceptual differences between the flow-adjustment processes used and with data processing methods. The decreasing trends in TSS, TP, and OP concentrations are likely related to conservation measures implemented in the basin. However, dilution effects from wet climate or additional tile drainage cannot be ruled out. The increasing trend in NO3-N concentrations was likely due to increased drainage in the basin. Since the Minnesota River is the main source of sediments to the Mississippi River, this study also addressed the rapid filling of Lake Pepin on the Mississippi River and found the likely cause to be increased flow due to recent wet climate in the region. Copyright ?? 2009 by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America. All rights reserved.

A Nonparametric Framework for Comparing Trends and Gaps across Tests

ERIC Educational Resources Information Center

Ho, Andrew Dean

2009-01-01

Problems of scale typically arise when comparing test score trends, gaps, and gap trends across different tests. To overcome some of these difficulties, test score distributions on the same score scale can be represented by nonparametric graphs or statistics that are invariant under monotone scale transformations. This article motivates and then…

A Bayesian Beta-Mixture Model for Nonparametric IRT (BBM-IRT)

ERIC Educational Resources Information Center

Arenson, Ethan A.; Karabatsos, George

2017-01-01

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

Non-parametric directionality analysis - Extension for removal of a single common predictor and application to time series.

PubMed

Halliday, David M; Senik, Mohd Harizal; Stevenson, Carl W; Mason, Rob

2016-08-01

The ability to infer network structure from multivariate neuronal signals is central to computational neuroscience. Directed network analyses typically use parametric approaches based on auto-regressive (AR) models, where networks are constructed from estimates of AR model parameters. However, the validity of using low order AR models for neurophysiological signals has been questioned. A recent article introduced a non-parametric approach to estimate directionality in bivariate data, non-parametric approaches are free from concerns over model validity. We extend the non-parametric framework to include measures of directed conditional independence, using scalar measures that decompose the overall partial correlation coefficient summatively by direction, and a set of functions that decompose the partial coherence summatively by direction. A time domain partial correlation function allows both time and frequency views of the data to be constructed. The conditional independence estimates are conditioned on a single predictor. The framework is applied to simulated cortical neuron networks and mixtures of Gaussian time series data with known interactions. It is applied to experimental data consisting of local field potential recordings from bilateral hippocampus in anaesthetised rats. The framework offers a non-parametric approach to estimation of directed interactions in multivariate neuronal recordings, and increased flexibility in dealing with both spike train and time series data. The framework offers a novel alternative non-parametric approach to estimate directed interactions in multivariate neuronal recordings, and is applicable to spike train and time series data. Copyright © 2016 Elsevier B.V. All rights reserved.

Levy Matrices and Financial Covariances

NASA Astrophysics Data System (ADS)

Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, Gabor; Zahed, Ismail

2003-10-01

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

Structural Analysis of Covariance and Correlation Matrices.

ERIC Educational Resources Information Center

Joreskog, Karl G.

1978-01-01

A general approach to analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.…

CADDIS Volume 4. Data Analysis: PECBO Appendix - R Scripts for Non-Parametric Regressions

EPA Pesticide Factsheets

Script for computing nonparametric regression analysis. Overview of using scripts to infer environmental conditions from biological observations, statistically estimating species-environment relationships, statistical scripts.

Dangers in Using Analysis of Covariance Procedures.

ERIC Educational Resources Information Center

Campbell, Kathleen T.

Problems associated with the use of analysis of covariance (ANCOVA) as a statistical control technique are explained. Three problems relate to the use of "OVA" methods (analysis of variance, analysis of covariance, multivariate analysis of variance, and multivariate analysis of covariance) in general. These are: (1) the wasting of information when…

Nuclear Cataract Shows Significant Familial Aggregation in an Older Population after Adjustment for Possible Shared Environmental Factors

PubMed Central

Congdon, Nathan; Broman, Karl W.; Lai, Hong; Munoz, Beatriz; Bowie, Heidi; Gilber, Donna; Wojciechowski, Robert; Alston, Christine; West, Sheila K.

2011-01-01

Purpose To quantify the association between siblings in age-related nuclear cataract, after adjusting for known environmental and personal risk factors. Methods All participants (probands) in the Salisbury Eye Evaluation (SEE) project and their locally resident siblings underwent digital slit lamp photography and were administered a questionnaire to assess risk factors for cataract including: age, gender, lifetime sun exposure, smoking and diabetes history, and use of alcohol and medications such as estrogens and steroids. In addition, blood pressure, body mass index, and serum antioxidants were measured in all participants. Lens photographs were graded by trained observers masked to the subjects' identity, using the Wilmer Cataract Grading System. The odds ratio for siblings for affectedness with nuclear cataract and the sibling correlation of nuclear cataract grade, after adjusting for covariates, were estimated with generalized estimating equations. Results Among 307 probands (mean age, 77.6 ± 4.5 years) and 434 full siblings (mean age, 72.4 ± 7.4 years), the average sibship size was 2.7 per family. After adjustment for covariates, the probability of development of nuclear cataract was significantly increased (odds ratio [OR] = 2.07, 95% confidence interval [CI], 1.30–3.30) among individuals with a sibling with nuclear cataract (nuclear grade ≥ 3.0). The final fitted model indicated a magnitude of heritability for nuclear cataract of 35.6% (95% CI: 21.0%–50.3%) after adjustment for the covariates. Conclusions Findings in this study are consistent with a genetic effect for age-related nuclear cataract, a common and clinically significant form of lens opacity. PMID:15223793

Estimation of Spatial Dynamic Nonparametric Durbin Models with Fixed Effects

ERIC Educational Resources Information Center

Qian, Minghui; Hu, Ridong; Chen, Jianwei

2016-01-01

Spatial panel data models have been widely studied and applied in both scientific and social science disciplines, especially in the analysis of spatial influence. In this paper, we consider the spatial dynamic nonparametric Durbin model (SDNDM) with fixed effects, which takes the nonlinear factors into account base on the spatial dynamic panel…

Nonparametric Item Response Curve Estimation with Correction for Measurement Error

ERIC Educational Resources Information Center

Guo, Hongwen; Sinharay, Sandip

2011-01-01

Nonparametric or kernel regression estimation of item response curves (IRCs) is often used in item analysis in testing programs. These estimates are biased when the observed scores are used as the regressor because the observed scores are contaminated by measurement error. Accuracy of this estimation is a concern theoretically and operationally.…

Covariant harmonic oscillators: 1973 revisited

NASA Technical Reports Server (NTRS)

Noz, M. E.

1993-01-01

Using the relativistic harmonic oscillator, a physical basis is given to the phenomenological wave function of Yukawa which is covariant and normalizable. It is shown that this wave function can be interpreted in terms of the unitary irreducible representations of the Poincare group. The transformation properties of these covariant wave functions are also demonstrated.

Propensity score method: a non-parametric technique to reduce model dependence

PubMed Central

2017-01-01

Propensity score analysis (PSA) is a powerful technique that it balances pretreatment covariates, making the causal effect inference from observational data as reliable as possible. The use of PSA in medical literature has increased exponentially in recent years, and the trend continue to rise. The article introduces rationales behind PSA, followed by illustrating how to perform PSA in R with MatchIt package. There are a variety of methods available for PS matching such as nearest neighbors, full matching, exact matching and genetic matching. The task can be easily done by simply assigning a string value to the method argument in the matchit() function. The generic summary() and plot() functions can be applied to an object of class matchit to check covariate balance after matching. Furthermore, there is a useful package PSAgraphics that contains several graphical functions to check covariate balance between treatment groups across strata. If covariate balance is not achieved, one can modify model specifications or use other techniques such as random forest and recursive partitioning to better represent the underlying structure between pretreatment covariates and treatment assignment. The process can be repeated until the desirable covariate balance is achieved. PMID:28164092

Least-Squares Neutron Spectral Adjustment with STAYSL PNNL

NASA Astrophysics Data System (ADS)

Greenwood, L. R.; Johnson, C. D.

2016-02-01

The STAYSL PNNL computer code, a descendant of the STAY'SL code [1], performs neutron spectral adjustment of a starting neutron spectrum, applying a least squares method to determine adjustments based on saturated activation rates, neutron cross sections from evaluated nuclear data libraries, and all associated covariances. STAYSL PNNL is provided as part of a comprehensive suite of programs [2], where additional tools in the suite are used for assembling a set of nuclear data libraries and determining all required corrections to the measured data to determine saturated activation rates. Neutron cross section and covariance data are taken from the International Reactor Dosimetry File (IRDF-2002) [3], which was sponsored by the International Atomic Energy Agency (IAEA), though work is planned to update to data from the IAEA's International Reactor Dosimetry and Fusion File (IRDFF) [4]. The nuclear data and associated covariances are extracted from IRDF-2002 using the third-party NJOY99 computer code [5]. The NJpp translation code converts the extracted data into a library data array format suitable for use as input to STAYSL PNNL. The software suite also includes three utilities to calculate corrections to measured activation rates. Neutron self-shielding corrections are calculated as a function of neutron energy with the SHIELD code and are applied to the group cross sections prior to spectral adjustment, thus making the corrections independent of the neutron spectrum. The SigPhi Calculator is a Microsoft Excel spreadsheet used for calculating saturated activation rates from raw gamma activities by applying corrections for gamma self-absorption, neutron burn-up, and the irradiation history. Gamma self-absorption and neutron burn-up corrections are calculated (iteratively in the case of the burn-up) within the SigPhi Calculator spreadsheet. The irradiation history corrections are calculated using the BCF computer code and are inserted into the SigPhi Calculator

A simulation study of nonparametric total deviation index as a measure of agreement based on quantile regression.

PubMed

Lin, Lawrence; Pan, Yi; Hedayat, A S; Barnhart, Huiman X; Haber, Michael

2016-01-01

Total deviation index (TDI) captures a prespecified quantile of the absolute deviation of paired observations from raters, observers, methods, assays, instruments, etc. We compare the performance of TDI using nonparametric quantile regression to the TDI assuming normality (Lin, 2000). This simulation study considers three distributions: normal, Poisson, and uniform at quantile levels of 0.8 and 0.9 for cases with and without contamination. Study endpoints include the bias of TDI estimates (compared with their respective theoretical values), standard error of TDI estimates (compared with their true simulated standard errors), and test size (compared with 0.05), and power. Nonparametric TDI using quantile regression, although it slightly underestimates and delivers slightly less power for data without contamination, works satisfactorily under all simulated cases even for moderate (say, ≥40) sample sizes. The performance of the TDI based on a quantile of 0.8 is in general superior to that of 0.9. The performances of nonparametric and parametric TDI methods are compared with a real data example. Nonparametric TDI can be very useful when the underlying distribution on the difference is not normal, especially when it has a heavy tail.

Bootstrap Prediction Intervals in Non-Parametric Regression with Applications to Anomaly Detection

NASA Technical Reports Server (NTRS)

Kumar, Sricharan; Srivistava, Ashok N.

2012-01-01

Prediction intervals provide a measure of the probable interval in which the outputs of a regression model can be expected to occur. Subsequently, these prediction intervals can be used to determine if the observed output is anomalous or not, conditioned on the input. In this paper, a procedure for determining prediction intervals for outputs of nonparametric regression models using bootstrap methods is proposed. Bootstrap methods allow for a non-parametric approach to computing prediction intervals with no specific assumptions about the sampling distribution of the noise or the data. The asymptotic fidelity of the proposed prediction intervals is theoretically proved. Subsequently, the validity of the bootstrap based prediction intervals is illustrated via simulations. Finally, the bootstrap prediction intervals are applied to the problem of anomaly detection on aviation data.

Least squares regression methods for clustered ROC data with discrete covariates.

PubMed

Tang, Liansheng Larry; Zhang, Wei; Li, Qizhai; Ye, Xuan; Chan, Leighton

2016-07-01

The receiver operating characteristic (ROC) curve is a popular tool to evaluate and compare the accuracy of diagnostic tests to distinguish the diseased group from the nondiseased group when test results from tests are continuous or ordinal. A complicated data setting occurs when multiple tests are measured on abnormal and normal locations from the same subject and the measurements are clustered within the subject. Although least squares regression methods can be used for the estimation of ROC curve from correlated data, how to develop the least squares methods to estimate the ROC curve from the clustered data has not been studied. Also, the statistical properties of the least squares methods under the clustering setting are unknown. In this article, we develop the least squares ROC methods to allow the baseline and link functions to differ, and more importantly, to accommodate clustered data with discrete covariates. The methods can generate smooth ROC curves that satisfy the inherent continuous property of the true underlying curve. The least squares methods are shown to be more efficient than the existing nonparametric ROC methods under appropriate model assumptions in simulation studies. We apply the methods to a real example in the detection of glaucomatous deterioration. We also derive the asymptotic properties of the proposed methods. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Precomputing Process Noise Covariance for Onboard Sequential Filters

NASA Technical Reports Server (NTRS)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis studies is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

Precomputing Process Noise Covariance for Onboard Sequential Filters

NASA Technical Reports Server (NTRS)

Olson, Corwin G.; Russell, Ryan P.; Carpenter, J. Russell

2017-01-01

Process noise is often used in estimation filters to account for unmodeled and mismodeled accelerations in the dynamics. The process noise covariance acts to inflate the state covariance over propagation intervals, increasing the uncertainty in the state. In scenarios where the acceleration errors change significantly over time, the standard process noise covariance approach can fail to provide effective representation of the state and its uncertainty. Consider covariance analysis techniques provide a method to precompute a process noise covariance profile along a reference trajectory, using known model parameter uncertainties. The process noise covariance profile allows significantly improved state estimation and uncertainty representation over the traditional formulation. As a result, estimation performance on par with the consider filter is achieved for trajectories near the reference trajectory without the additional computational cost of the consider filter. The new formulation also has the potential to significantly reduce the trial-and-error tuning currently required of navigation analysts. A linear estimation problem as described in several previous consider covariance analysis publications is used to demonstrate the effectiveness of the precomputed process noise covariance, as well as a nonlinear descent scenario at the asteroid Bennu with optical navigation.

Transformation-invariant and nonparametric monotone smooth estimation of ROC curves.

PubMed

Du, Pang; Tang, Liansheng

2009-01-30

When a new diagnostic test is developed, it is of interest to evaluate its accuracy in distinguishing diseased subjects from non-diseased subjects. The accuracy of the test is often evaluated by receiver operating characteristic (ROC) curves. Smooth ROC estimates are often preferable for continuous test results when the underlying ROC curves are in fact continuous. Nonparametric and parametric methods have been proposed by various authors to obtain smooth ROC curve estimates. However, there are certain drawbacks with the existing methods. Parametric methods need specific model assumptions. Nonparametric methods do not always satisfy the inherent properties of the ROC curves, such as monotonicity and transformation invariance. In this paper we propose a monotone spline approach to obtain smooth monotone ROC curves. Our method ensures important inherent properties of the underlying ROC curves, which include monotonicity, transformation invariance, and boundary constraints. We compare the finite sample performance of the newly proposed ROC method with other ROC smoothing methods in large-scale simulation studies. We illustrate our method through a real life example. Copyright (c) 2008 John Wiley & Sons, Ltd.

UDU/T/ covariance factorization for Kalman filtering

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1980-01-01

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

Low-dimensional Representation of Error Covariance

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.; Todling, Ricardo; Marchesin, Dan

2000-01-01

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Covariance hypotheses for LANDSAT data

NASA Technical Reports Server (NTRS)

Decell, H. P.; Peters, C.

1983-01-01

Two covariance hypotheses are considered for LANDSAT data acquired by sampling fields, one an autoregressive covariance structure and the other the hypothesis of exchangeability. A minimum entropy approximation of the first structure by the second is derived and shown to have desirable properties for incorporation into a mixture density estimation procedure. Results of a rough test of the exchangeability hypothesis are presented.

Order-Constrained Bayes Inference for Dichotomous Models of Unidimensional Nonparametric IRT

ERIC Educational Resources Information Center

Karabatsos, George; Sheu, Ching-Fan

2004-01-01

This study introduces an order-constrained Bayes inference framework useful for analyzing data containing dichotomous scored item responses, under the assumptions of either the monotone homogeneity model or the double monotonicity model of nonparametric item response theory (NIRT). The framework involves the implementation of Gibbs sampling to…

Nonparametric Residue Analysis of Dynamic PET Data With Application to Cerebral FDG Studies in Normals.

PubMed

O'Sullivan, Finbarr; Muzi, Mark; Spence, Alexander M; Mankoff, David M; O'Sullivan, Janet N; Fitzgerald, Niall; Newman, George C; Krohn, Kenneth A

2009-06-01

Kinetic analysis is used to extract metabolic information from dynamic positron emission tomography (PET) uptake data. The theory of indicator dilutions, developed in the seminal work of Meier and Zierler (1954), provides a probabilistic framework for representation of PET tracer uptake data in terms of a convolution between an arterial input function and a tissue residue. The residue is a scaled survival function associated with tracer residence in the tissue. Nonparametric inference for the residue, a deconvolution problem, provides a novel approach to kinetic analysis-critically one that is not reliant on specific compartmental modeling assumptions. A practical computational technique based on regularized cubic B-spline approximation of the residence time distribution is proposed. Nonparametric residue analysis allows formal statistical evaluation of specific parametric models to be considered. This analysis needs to properly account for the increased flexibility of the nonparametric estimator. The methodology is illustrated using data from a series of cerebral studies with PET and fluorodeoxyglucose (FDG) in normal subjects. Comparisons are made between key functionals of the residue, tracer flux, flow, etc., resulting from a parametric (the standard two-compartment of Phelps et al. 1979) and a nonparametric analysis. Strong statistical evidence against the compartment model is found. Primarily these differences relate to the representation of the early temporal structure of the tracer residence-largely a function of the vascular supply network. There are convincing physiological arguments against the representations implied by the compartmental approach but this is the first time that a rigorous statistical confirmation using PET data has been reported. The compartmental analysis produces suspect values for flow but, notably, the impact on the metabolic flux, though statistically significant, is limited to deviations on the order of 3%-4%. The general

On non-parametric maximum likelihood estimation of the bivariate survivor function.

PubMed

Prentice, R L

The likelihood function for the bivariate survivor function F, under independent censorship, is maximized to obtain a non-parametric maximum likelihood estimator &Fcirc;. &Fcirc; may or may not be unique depending on the configuration of singly- and doubly-censored pairs. The likelihood function can be maximized by placing all mass on the grid formed by the uncensored failure times, or half lines beyond the failure time grid, or in the upper right quadrant beyond the grid. By accumulating the mass along lines (or regions) where the likelihood is flat, one obtains a partially maximized likelihood as a function of parameters that can be uniquely estimated. The score equations corresponding to these point mass parameters are derived, using a Lagrange multiplier technique to ensure unit total mass, and a modified Newton procedure is used to calculate the parameter estimates in some limited simulation studies. Some considerations for the further development of non-parametric bivariate survivor function estimators are briefly described.

Using a DEA Management Tool through a Nonparametric Approach: An Examination of Urban-Rural Effects on Thai School Efficiency

ERIC Educational Resources Information Center

Kantabutra, Sangchan

2009-01-01

This paper examines urban-rural effects on public upper-secondary school efficiency in northern Thailand. In the study, efficiency was measured by a nonparametric technique, data envelopment analysis (DEA). Urban-rural effects were examined through a Mann-Whitney nonparametric statistical test. Results indicate that urban schools appear to have…

Quantifying the impact of time-varying baseline risk adjustment in the self-controlled risk interval design.

PubMed

Li, Lingling; Kulldorff, Martin; Russek-Cohen, Estelle; Kawai, Alison Tse; Hua, Wei

2015-12-01

The self-controlled risk interval design is commonly used to assess the association between an acute exposure and an adverse event of interest, implicitly adjusting for fixed, non-time-varying covariates. Explicit adjustment needs to be made for time-varying covariates, for example, age in young children. It can be performed via either a fixed or random adjustment. The random-adjustment approach can provide valid point and interval estimates but requires access to individual-level data for an unexposed baseline sample. The fixed-adjustment approach does not have this requirement and will provide a valid point estimate but may underestimate the variance. We conducted a comprehensive simulation study to evaluate their performance. We designed the simulation study using empirical data from the Food and Drug Administration-sponsored Mini-Sentinel Post-licensure Rapid Immunization Safety Monitoring Rotavirus Vaccines and Intussusception study in children 5-36.9 weeks of age. The time-varying confounder is age. We considered a variety of design parameters including sample size, relative risk, time-varying baseline risks, and risk interval length. The random-adjustment approach has very good performance in almost all considered settings. The fixed-adjustment approach can be used as a good alternative when the number of events used to estimate the time-varying baseline risks is at least the number of events used to estimate the relative risk, which is almost always the case. We successfully identified settings in which the fixed-adjustment approach can be used as a good alternative and provided guidelines on the selection and implementation of appropriate analyses for the self-controlled risk interval design. Copyright © 2015 John Wiley & Sons, Ltd.

Non-parametric transient classification using adaptive wavelets

NASA Astrophysics Data System (ADS)

Varughese, Melvin M.; von Sachs, Rainer; Stephanou, Michael; Bassett, Bruce A.

2015-11-01

Classifying transients based on multiband light curves is a challenging but crucial problem in the era of GAIA and Large Synoptic Sky Telescope since the sheer volume of transients will make spectroscopic classification unfeasible. We present a non-parametric classifier that predicts the transient's class given training data. It implements two novel components: the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients - as well as the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The classifier is simple to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant. Hence, BAGIDIS does not need the light curves to be aligned to extract features. Further, BAGIDIS is non-parametric so it can be used effectively in blind searches for new objects. We demonstrate the effectiveness of our classifier against the Supernova Photometric Classification Challenge to correctly classify supernova light curves as Type Ia or non-Ia. We train our classifier on the spectroscopically confirmed subsample (which is not representative) and show that it works well for supernova with observed light-curve time spans greater than 100 d (roughly 55 per cent of the data set). For such data, we obtain a Ia efficiency of 80.5 per cent and a purity of 82.4 per cent, yielding a highly competitive challenge score of 0.49. This indicates that our `model-blind' approach may be particularly suitable for the general classification of astronomical transients in the era of large synoptic sky surveys.

Pharmacokinetic modelling of intravenous tobramycin in adolescent and adult patients with cystic fibrosis using the nonparametric expectation maximization (NPEM) algorithm.

PubMed

Touw, D J; Vinks, A A; Neef, C

1997-06-01

The availability of personal computer programs for individualizing drug dosage regimens has stimulated the interest in modelling population pharmacokinetics. Data from 82 adolescent and adult patients with cystic fibrosis (CF) who were treated with intravenous tobramycin because of an exacerbation of their pulmonary infection were analysed with a non-parametric expectation maximization (NPEM) algorithm. This algorithm estimates the entire discrete joint probability density of the pharmacokinetic parameters. It also provides traditional parametric statistics such as the means, standard deviation, median, covariances and correlations among the various parameters. It also provides graphic-2- and 3-dimensional representations of the marginal densities of the parameters investigated. Several models for intravenous tobramycin in adolescent and adult patients with CF were compared. Covariates were total body weight (for the volume of distribution) and creatinine clearance (for the total body clearance and elimination rate). Because of lack of data on patients with poor renal function, restricted models with non-renal clearance and the non-renal elimination rate constant fixed at literature values of 0.15 L/h and 0.01 h-1 were also included. In this population, intravenous tobramycin could be best described by median (+/-dispersion factor) volume of distribution per unit of total body weight of 0.28 +/- 0.05 L/kg, elimination rate constant of 0.25 +/- 0.10 h-1 and elimination rate constant per unit of creatinine clearance of 0.0008 +/- 0.0009 h-1/(ml/min/1.73 m2). Analysis of populations of increasing size showed that using a restricted model with a non-renal elimination rate constant fixed at 0.01 h-1, a model based on a population of only 10 to 20 patients, contained parameter values similar to those of the entire population and, using the full model, a larger population (at least 40 patients) was needed.

Summarizing techniques that combine three non-parametric scores to detect disease-associated 2-way SNP-SNP interactions.

PubMed

Sengupta Chattopadhyay, Amrita; Hsiao, Ching-Lin; Chang, Chien Ching; Lian, Ie-Bin; Fann, Cathy S J

2014-01-01

Identifying susceptibility genes that influence complex diseases is extremely difficult because loci often influence the disease state through genetic interactions. Numerous approaches to detect disease-associated SNP-SNP interactions have been developed, but none consistently generates high-quality results under different disease scenarios. Using summarizing techniques to combine a number of existing methods may provide a solution to this problem. Here we used three popular non-parametric methods-Gini, absolute probability difference (APD), and entropy-to develop two novel summary scores, namely principle component score (PCS) and Z-sum score (ZSS), with which to predict disease-associated genetic interactions. We used a simulation study to compare performance of the non-parametric scores, the summary scores, the scaled-sum score (SSS; used in polymorphism interaction analysis (PIA)), and the multifactor dimensionality reduction (MDR). The non-parametric methods achieved high power, but no non-parametric method outperformed all others under a variety of epistatic scenarios. PCS and ZSS, however, outperformed MDR. PCS, ZSS and SSS displayed controlled type-I-errors (<0.05) compared to GS, APDS, ES (>0.05). A real data study using the genetic-analysis-workshop 16 (GAW 16) rheumatoid arthritis dataset identified a number of interesting SNP-SNP interactions. © 2013 Elsevier B.V. All rights reserved.

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Form of the manifestly covariant Lagrangian

NASA Astrophysics Data System (ADS)

Johns, Oliver Davis

1985-10-01

The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Non-parametric wall model and methods of identifying boundary conditions for moments in gas flow equations

NASA Astrophysics Data System (ADS)

Liao, Meng; To, Quy-Dong; Léonard, Céline; Monchiet, Vincent

2018-03-01

In this paper, we use the molecular dynamics simulation method to study gas-wall boundary conditions. Discrete scattering information of gas molecules at the wall surface is obtained from collision simulations. The collision data can be used to identify the accommodation coefficients for parametric wall models such as Maxwell and Cercignani-Lampis scattering kernels. Since these scattering kernels are based on a limited number of accommodation coefficients, we adopt non-parametric statistical methods to construct the kernel to overcome these issues. Different from parametric kernels, the non-parametric kernels require no parameter (i.e. accommodation coefficients) and no predefined distribution. We also propose approaches to derive directly the Navier friction and Kapitza thermal resistance coefficients as well as other interface coefficients associated with moment equations from the non-parametric kernels. The methods are applied successfully to systems composed of CH4 or CO2 and graphite, which are of interest to the petroleum industry.

Cross-population myelination covariance of human cerebral cortex.

PubMed

Ma, Zhiwei; Zhang, Nanyin

2017-09-01

Cross-population covariance of brain morphometric quantities provides a measure of interareal connectivity, as it is believed to be determined by the coordinated neurodevelopment of connected brain regions. Although useful, structural covariance analysis predominantly employed bulky morphological measures with mixed compartments, whereas studies of the structural covariance of any specific subdivisions such as myelin are rare. Characterizing myelination covariance is of interest, as it will reveal connectivity patterns determined by coordinated development of myeloarchitecture between brain regions. Using myelin content MRI maps from the Human Connectome Project, here we showed that the cortical myelination covariance was highly reproducible, and exhibited a brain organization similar to that previously revealed by other connectivity measures. Additionally, the myelination covariance network shared common topological features of human brain networks such as small-worldness. Furthermore, we found that the correlation between myelination covariance and resting-state functional connectivity (RSFC) was uniform within each resting-state network (RSN), but could considerably vary across RSNs. Interestingly, this myelination covariance-RSFC correlation was appreciably stronger in sensory and motor networks than cognitive and polymodal association networks, possibly due to their different circuitry structures. This study has established a new brain connectivity measure specifically related to axons, and this measure can be valuable to investigating coordinated myeloarchitecture development. Hum Brain Mapp 38:4730-4743, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

A Bayesian nonparametric approach to dynamical noise reduction

NASA Astrophysics Data System (ADS)

Kaloudis, Konstantinos; Hatjispyros, Spyridon J.

2018-06-01

We propose a Bayesian nonparametric approach for the noise reduction of a given chaotic time series contaminated by dynamical noise, based on Markov Chain Monte Carlo methods. The underlying unknown noise process (possibly) exhibits heavy tailed behavior. We introduce the Dynamic Noise Reduction Replicator model with which we reconstruct the unknown dynamic equations and in parallel we replicate the dynamics under reduced noise level dynamical perturbations. The dynamic noise reduction procedure is demonstrated specifically in the case of polynomial maps. Simulations based on synthetic time series are presented.

Dimension from covariance matrices.

PubMed

Carroll, T L; Byers, J M

2017-02-01

We describe a method to estimate embedding dimension from a time series. This method includes an estimate of the probability that the dimension estimate is valid. Such validity estimates are not common in algorithms for calculating the properties of dynamical systems. The algorithm described here compares the eigenvalues of covariance matrices created from an embedded signal to the eigenvalues for a covariance matrix of a Gaussian random process with the same dimension and number of points. A statistical test gives the probability that the eigenvalues for the embedded signal did not come from the Gaussian random process.

Condition Number Regularized Covariance Estimation.

PubMed

Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala

2013-06-01

Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the "large p small n " setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required.

Semiparametric Bayesian analysis of gene-environment interactions with error in measurement of environmental covariates and missing genetic data.

PubMed

Lobach, Iryna; Mallick, Bani; Carroll, Raymond J

2011-01-01

Case-control studies are widely used to detect gene-environment interactions in the etiology of complex diseases. Many variables that are of interest to biomedical researchers are difficult to measure on an individual level, e.g. nutrient intake, cigarette smoking exposure, long-term toxic exposure. Measurement error causes bias in parameter estimates, thus masking key features of data and leading to loss of power and spurious/masked associations. We develop a Bayesian methodology for analysis of case-control studies for the case when measurement error is present in an environmental covariate and the genetic variable has missing data. This approach offers several advantages. It allows prior information to enter the model to make estimation and inference more precise. The environmental covariates measured exactly are modeled completely nonparametrically. Further, information about the probability of disease can be incorporated in the estimation procedure to improve quality of parameter estimates, what cannot be done in conventional case-control studies. A unique feature of the procedure under investigation is that the analysis is based on a pseudo-likelihood function therefore conventional Bayesian techniques may not be technically correct. We propose an approach using Markov Chain Monte Carlo sampling as well as a computationally simple method based on an asymptotic posterior distribution. Simulation experiments demonstrated that our method produced parameter estimates that are nearly unbiased even for small sample sizes. An application of our method is illustrated using a population-based case-control study of the association between calcium intake with the risk of colorectal adenoma development.

Applications of non-parametric statistics and analysis of variance on sample variances

NASA Technical Reports Server (NTRS)

Myers, R. H.

1981-01-01

Nonparametric methods that are available for NASA-type applications are discussed. An attempt will be made here to survey what can be used, to attempt recommendations as to when each would be applicable, and to compare the methods, when possible, with the usual normal-theory procedures that are avavilable for the Gaussion analog. It is important here to point out the hypotheses that are being tested, the assumptions that are being made, and limitations of the nonparametric procedures. The appropriateness of doing analysis of variance on sample variances are also discussed and studied. This procedure is followed in several NASA simulation projects. On the surface this would appear to be reasonably sound procedure. However, difficulties involved center around the normality problem and the basic homogeneous variance assumption that is mase in usual analysis of variance problems. These difficulties discussed and guidelines given for using the methods.

Adjusting for multiple prognostic factors in the analysis of randomised trials

PubMed Central

2013-01-01

Background When multiple prognostic factors are adjusted for in the analysis of a randomised trial, it is unclear (1) whether it is necessary to account for each of the strata, formed by all combinations of the prognostic factors (stratified analysis), when randomisation has been balanced within each stratum (stratified randomisation), or whether adjusting for the main effects alone will suffice, and (2) the best method of adjustment in terms of type I error rate and power, irrespective of the randomisation method. Methods We used simulation to (1) determine if a stratified analysis is necessary after stratified randomisation, and (2) to compare different methods of adjustment in terms of power and type I error rate. We considered the following methods of analysis: adjusting for covariates in a regression model, adjusting for each stratum using either fixed or random effects, and Mantel-Haenszel or a stratified Cox model depending on outcome. Results Stratified analysis is required after stratified randomisation to maintain correct type I error rates when (a) there are strong interactions between prognostic factors, and (b) there are approximately equal number of patients in each stratum. However, simulations based on real trial data found that type I error rates were unaffected by the method of analysis (stratified vs unstratified), indicating these conditions were not met in real datasets. Comparison of different analysis methods found that with small sample sizes and a binary or time-to-event outcome, most analysis methods lead to either inflated type I error rates or a reduction in power; the lone exception was a stratified analysis using random effects for strata, which gave nominal type I error rates and adequate power. Conclusions It is unlikely that a stratified analysis is necessary after stratified randomisation except in extreme scenarios. Therefore, the method of analysis (accounting for the strata, or adjusting only for the covariates) will not

Short-time windowed covariance: A metric for identifying non-stationary, event-related covariant cortical sites

PubMed Central

Blakely, Timothy; Ojemann, Jeffrey G.; Rao, Rajesh P.N.

2014-01-01

Background Electrocorticography (ECoG) signals can provide high spatio-temporal resolution and high signal to noise ratio recordings of local neural activity from the surface of the brain. Previous studies have shown that broad-band, spatially focal, high-frequency increases in ECoG signals are highly correlated with movement and other cognitive tasks and can be volitionally modulated. However, significant additional information may be present in inter-electrode interactions, but adding additional higher order inter-electrode interactions can be impractical from a computational aspect, if not impossible. New method In this paper we present a new method of calculating high frequency interactions between electrodes called Short-Time Windowed Covariance (STWC) that builds on mathematical techniques currently used in neural signal analysis, along with an implementation that accelerates the algorithm by orders of magnitude by leveraging commodity, off-the-shelf graphics processing unit (GPU) hardware. Results Using the hardware-accelerated implementation of STWC, we identify many types of event-related inter-electrode interactions from human ECoG recordings on global and local scales that have not been identified by previous methods. Unique temporal patterns are observed for digit flexion in both low- (10 mm spacing) and high-resolution (3 mm spacing) electrode arrays. Comparison with existing methods Covariance is a commonly used metric for identifying correlated signals, but the standard covariance calculations do not allow for temporally varying covariance. In contrast STWC allows and identifies event-driven changes in covariance without identifying spurious noise correlations. Conclusions: STWC can be used to identify event-related neural interactions whose high computational load is well suited to GPU capabilities. PMID:24211499

Heavy and Heavy-Light Mesons in the Covariant Spectator Theory

NASA Astrophysics Data System (ADS)

Stadler, Alfred; Leitão, Sofia; Peña, M. T.; Biernat, Elmar P.

2018-05-01

The masses and vertex functions of heavy and heavy-light mesons, described as quark-antiquark bound states, are calculated with the Covariant Spectator Theory (CST). We use a kernel with an adjustable mixture of Lorentz scalar, pseudoscalar, and vector linear confining interaction, together with a one-gluon-exchange kernel. A series of fits to the heavy and heavy-light meson spectrum were calculated, and we discuss what conclusions can be drawn from it, especially about the Lorentz structure of the kernel. We also apply the Brodsky-Huang-Lepage prescription to express the CST wave functions for heavy quarkonia in terms of light-front variables. They agree remarkably well with light-front wave functions obtained in the Hamiltonian basis light-front quantization approach, even in excited states.

A Bayesian Nonparametric Meta-Analysis Model

ERIC Educational Resources Information Center

Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G.

2015-01-01

In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall…

Exponential series approaches for nonparametric graphical models

NASA Astrophysics Data System (ADS)

Janofsky, Eric

Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of exponential series which approximates the log density by a finite-dimensional exponential family with the number of sufficient statistics increasing with the sample size. We consider two approaches to estimating these models. The first is regularized maximum likelihood. This involves optimizing the sum of the log-likelihood of the data and a sparsity-inducing regularizer. We then propose a variational approximation to the likelihood based on tree-reweighted, nonparametric message passing. This approximation allows for upper bounds on risk estimates, leverages parallelization and is scalable to densities on hundreds of nodes. We show how the regularized variational MLE may be estimated using a proximal gradient algorithm. We then consider estimation using regularized score matching. This approach uses an alternative scoring rule to the log-likelihood, which obviates the need to compute the normalizing constant of the distribution. For general continuous-valued exponential families, we provide parameter and edge consistency results. As a special case we detail a new approach to sparse precision matrix estimation which has statistical performance competitive with the graphical lasso and computational performance competitive with the state-of-the-art glasso algorithm. We then describe results for model selection in the nonparametric pairwise model using exponential series. The regularized score matching problem is shown to be a convex program; we provide scalable algorithms based on consensus alternating direction method of multipliers (ADMM) and coordinate-wise descent. We use simulations to compare our

Feature Augmentation via Nonparametrics and Selection (FANS) in High-Dimensional Classification.

PubMed

Fan, Jianqing; Feng, Yang; Jiang, Jiancheng; Tong, Xin

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.

Feature Augmentation via Nonparametrics and Selection (FANS) in High-Dimensional Classification

PubMed Central

Feng, Yang; Jiang, Jiancheng; Tong, Xin

2015-01-01

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing. PMID:27185970

kruX: matrix-based non-parametric eQTL discovery

PubMed Central

2014-01-01

Background The Kruskal-Wallis test is a popular non-parametric statistical test for identifying expression quantitative trait loci (eQTLs) from genome-wide data due to its robustness against variations in the underlying genetic model and expression trait distribution, but testing billions of marker-trait combinations one-by-one can become computationally prohibitive. Results We developed kruX, an algorithm implemented in Matlab, Python and R that uses matrix multiplications to simultaneously calculate the Kruskal-Wallis test statistic for several millions of marker-trait combinations at once. KruX is more than ten thousand times faster than computing associations one-by-one on a typical human dataset. We used kruX and a dataset of more than 500k SNPs and 20k expression traits measured in 102 human blood samples to compare eQTLs detected by the Kruskal-Wallis test to eQTLs detected by the parametric ANOVA and linear model methods. We found that the Kruskal-Wallis test is more robust against data outliers and heterogeneous genotype group sizes and detects a higher proportion of non-linear associations, but is more conservative for calling additive linear associations. Conclusion kruX enables the use of robust non-parametric methods for massive eQTL mapping without the need for a high-performance computing infrastructure and is freely available from http://krux.googlecode.com. PMID:24423115

kruX: matrix-based non-parametric eQTL discovery.

PubMed

Qi, Jianlong; Asl, Hassan Foroughi; Björkegren, Johan; Michoel, Tom

2014-01-14

The Kruskal-Wallis test is a popular non-parametric statistical test for identifying expression quantitative trait loci (eQTLs) from genome-wide data due to its robustness against variations in the underlying genetic model and expression trait distribution, but testing billions of marker-trait combinations one-by-one can become computationally prohibitive. We developed kruX, an algorithm implemented in Matlab, Python and R that uses matrix multiplications to simultaneously calculate the Kruskal-Wallis test statistic for several millions of marker-trait combinations at once. KruX is more than ten thousand times faster than computing associations one-by-one on a typical human dataset. We used kruX and a dataset of more than 500k SNPs and 20k expression traits measured in 102 human blood samples to compare eQTLs detected by the Kruskal-Wallis test to eQTLs detected by the parametric ANOVA and linear model methods. We found that the Kruskal-Wallis test is more robust against data outliers and heterogeneous genotype group sizes and detects a higher proportion of non-linear associations, but is more conservative for calling additive linear associations. kruX enables the use of robust non-parametric methods for massive eQTL mapping without the need for a high-performance computing infrastructure and is freely available from http://krux.googlecode.com.

Social support and substitute voice acquisition on psychological adjustment among patients after laryngectomy.

PubMed

Kotake, Kumiko; Suzukamo, Yoshimi; Kai, Ichiro; Iwanaga, Kazuyo; Takahashi, Aya

2017-03-01

The objective is to clarify whether social support and acquisition of alternative voice enhance the psychological adjustment of laryngectomized patients and which part of the psychological adjustment structure would be influenced by social support. We contacted 1445 patients enrolled in a patient association using mail surveys and 679 patients agreed to participate in the study. The survey items included age, sex, occupation, post-surgery duration, communication method, psychological adjustment (by the Nottingham Adjustment Scale Japanese Laryngectomy Version: NAS-J-L), and the formal support (by Hospital Patient Satisfaction Questionnaire-25: HPSQ-25). Social support and communication methods were added to the three-tier structural model of psychological adjustment shown in our previous study, and a covariance structure analysis was conducted. Formal/informal supports and acquisition of alternative voice influence only the "recognition of oneself as voluntary agent", the first tier of the three-tier structure of psychological adjustment. The results suggest that social support and acquisition of alternative voice may enhance the recognition of oneself as voluntary agent and promote the psychological adjustment.

Students’ Covariational Reasoning in Solving Integrals’ Problems

NASA Astrophysics Data System (ADS)

Harini, N. V.; Fuad, Y.; Ekawati, R.

2018-01-01

Covariational reasoning plays an important role to indicate quantities vary in learning calculus. This study investigates students’ covariational reasoning during their studies concerning two covarying quantities in integral problem. Six undergraduate students were chosen to solve problems that involved interpreting and representing how quantities change in tandem. Interviews were conducted to reveal the students’ reasoning while solving covariational problems. The result emphasizes that undergraduate students were able to construct the relation of dependent variables that changes in tandem with the independent variable. However, students faced difficulty in forming images of continuously changing rates and could not accurately apply the concept of integrals. These findings suggest that learning calculus should be increased emphasis on coordinating images of two quantities changing in tandem about instantaneously rate of change and to promote conceptual knowledge in integral techniques.

A regularization corrected score method for nonlinear regression models with covariate error.

PubMed

Zucker, David M; Gorfine, Malka; Li, Yi; Tadesse, Mahlet G; Spiegelman, Donna

2013-03-01

Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer. Copyright © 2013, The International Biometric Society.

Gram-Schmidt algorithms for covariance propagation

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1977-01-01

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Gram-Schmidt algorithms for covariance propagation

NASA Technical Reports Server (NTRS)

Thornton, C. L.; Bierman, G. J.

1975-01-01

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Condition Number Regularized Covariance Estimation*

PubMed Central

Won, Joong-Ho; Lim, Johan; Kim, Seung-Jean; Rajaratnam, Bala

2012-01-01

Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the “large p small n” setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to do this, none of them address the ill-conditioning problem directly. In this paper, we propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumption on either the covariance matrix or its inverse are are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator, and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision-theoretic comparisons and in the financial portfolio optimization setting. The proposed approach has desirable properties, and can serve as a competitive procedure, especially when the sample size is small and when a well-conditioned estimator is required. PMID:23730197

Exact nonparametric confidence bands for the survivor function.

PubMed

Matthews, David

2013-10-12

A method to produce exact simultaneous confidence bands for the empirical cumulative distribution function that was first described by Owen, and subsequently corrected by Jager and Wellner, is the starting point for deriving exact nonparametric confidence bands for the survivor function of any positive random variable. We invert a nonparametric likelihood test of uniformity, constructed from the Kaplan-Meier estimator of the survivor function, to obtain simultaneous lower and upper bands for the function of interest with specified global confidence level. The method involves calculating a null distribution and associated critical value for each observed sample configuration. However, Noe recursions and the Van Wijngaarden-Decker-Brent root-finding algorithm provide the necessary tools for efficient computation of these exact bounds. Various aspects of the effect of right censoring on these exact bands are investigated, using as illustrations two observational studies of survival experience among non-Hodgkin's lymphoma patients and a much larger group of subjects with advanced lung cancer enrolled in trials within the North Central Cancer Treatment Group. Monte Carlo simulations confirm the merits of the proposed method of deriving simultaneous interval estimates of the survivor function across the entire range of the observed sample. This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. It was begun while the author was visiting the Department of Statistics, University of Auckland, and completed during a subsequent sojourn at the Medical Research Council Biostatistics Unit in Cambridge. The support of both institutions, in addition to that of NSERC and the University of Waterloo, is greatly appreciated.

Non-parametric correlative uncertainty quantification and sensitivity analysis: Application to a Langmuir bimolecular adsorption model

NASA Astrophysics Data System (ADS)

Feng, Jinchao; Lansford, Joshua; Mironenko, Alexander; Pourkargar, Davood Babaei; Vlachos, Dionisios G.; Katsoulakis, Markos A.

2018-03-01

We propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, are correlated and are limited in size (small data). The proposed mathematical methodology employs gradient-based methods to compute sensitivity indices. We observe that ranking influential parameters depends critically on whether or not correlations between parameters are taken into account. The impact of uncertainty in the correlation and the necessity of the proposed non-parametric perspective are demonstrated.

Conditional Covariance-Based Subtest Selection for DIMTEST

ERIC Educational Resources Information Center

Froelich, Amy G.; Habing, Brian

2008-01-01

DIMTEST is a nonparametric hypothesis-testing procedure designed to test the assumptions of a unidimensional and locally independent item response theory model. Several previous Monte Carlo studies have found that using linear factor analysis to select the assessment subtest for DIMTEST results in a moderate to severe loss of power when the exam…

Combined non-parametric and parametric approach for identification of time-variant systems

NASA Astrophysics Data System (ADS)

Dziedziech, Kajetan; Czop, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz

2018-03-01

Identification of systems, structures and machines with variable physical parameters is a challenging task especially when time-varying vibration modes are involved. The paper proposes a new combined, two-step - i.e. non-parametric and parametric - modelling approach in order to determine time-varying vibration modes based on input-output measurements. Single-degree-of-freedom (SDOF) vibration modes from multi-degree-of-freedom (MDOF) non-parametric system representation are extracted in the first step with the use of time-frequency wavelet-based filters. The second step involves time-varying parametric representation of extracted modes with the use of recursive linear autoregressive-moving-average with exogenous inputs (ARMAX) models. The combined approach is demonstrated using system identification analysis based on the experimental mass-varying MDOF frame-like structure subjected to random excitation. The results show that the proposed combined method correctly captures the dynamics of the analysed structure, using minimum a priori information on the model.

Earth Observation System Flight Dynamics System Covariance Realism

NASA Technical Reports Server (NTRS)

Zaidi, Waqar H.; Tracewell, David

2016-01-01

This presentation applies a covariance realism technique to the National Aeronautics and Space Administration (NASA) Earth Observation System (EOS) Aqua and Aura spacecraft based on inferential statistics. The technique consists of three parts: collection calculation of definitive state estimates through orbit determination, calculation of covariance realism test statistics at each covariance propagation point, and proper assessment of those test statistics.

Corrected goodness-of-fit test in covariance structure analysis.

PubMed

Hayakawa, Kazuhiko

2018-05-17

Many previous studies report simulation evidence that the goodness-of-fit test in covariance structure analysis or structural equation modeling suffers from the overrejection problem when the number of manifest variables is large compared with the sample size. In this study, we demonstrate that one of the tests considered in Browne (1974) can address this long-standing problem. We also propose a simple modification of Satorra and Bentler's mean and variance adjusted test for non-normal data. A Monte Carlo simulation is carried out to investigate the performance of the corrected tests in the context of a confirmatory factor model, a panel autoregressive model, and a cross-lagged panel (panel vector autoregressive) model. The simulation results reveal that the corrected tests overcome the overrejection problem and outperform existing tests in most cases. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Large Covariance Estimation by Thresholding Principal Orthogonal Complements.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2013-09-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.

Covariance NMR Processing and Analysis for Protein Assignment.

PubMed

Harden, Bradley J; Frueh, Dominique P

2018-01-01

During NMR resonance assignment it is often necessary to relate nuclei to one another indirectly, through their common correlations to other nuclei. Covariance NMR has emerged as a powerful technique to correlate such nuclei without relying on error-prone peak peaking. However, false-positive artifacts in covariance spectra have impeded a general application to proteins. We recently introduced pre- and postprocessing steps to reduce the prevalence of artifacts in covariance spectra, allowing for the calculation of a variety of 4D covariance maps obtained from diverse combinations of pairs of 3D spectra, and we have employed them to assign backbone and sidechain resonances in two large and challenging proteins. In this chapter, we present a detailed protocol describing how to (1) properly prepare existing 3D spectra for covariance, (2) understand and apply our processing script, and (3) navigate and interpret the resulting 4D spectra. We also provide solutions to a number of errors that may occur when using our script, and we offer practical advice when assigning difficult signals. We believe such 4D spectra, and covariance NMR in general, can play an integral role in the assignment of NMR signals.

Covariance Matrix Estimation for Massive MIMO

NASA Astrophysics Data System (ADS)

Upadhya, Karthik; Vorobyov, Sergiy A.

2018-04-01

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.

Assessing Goodness of Fit in Item Response Theory with Nonparametric Models: A Comparison of Posterior Probabilities and Kernel-Smoothing Approaches

ERIC Educational Resources Information Center

Sueiro, Manuel J.; Abad, Francisco J.

2011-01-01

The distance between nonparametric and parametric item characteristic curves has been proposed as an index of goodness of fit in item response theory in the form of a root integrated squared error index. This article proposes to use the posterior distribution of the latent trait as the nonparametric model and compares the performance of an index…

Performance of internal covariance estimators for cosmic shear correlation functions

DOE PAGES

Friedrich, O.; Seitz, S.; Eifler, T. F.; ...

2015-12-31

Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic shear two-point statistics. We demonstrate how to use log-normal simulations of the convergence field and the corresponding shear field to carry out realistic tests of internal covariance estimators and find that most estimators such as jackknife or sub-sample covariance can reach a satisfactory compromise between bias and variance of the estimated covariance. In a forecast for the complete, 5-year DES survey we show that internally estimated covariance matrices can provide a large fraction of the true uncertainties on cosmological parameters in a 2D cosmic shear analysis. The volume inside contours of constant likelihood in themore » $$\\Omega_m$$-$$\\sigma_8$$ plane as measured with internally estimated covariance matrices is on average $$\\gtrsim 85\\%$$ of the volume derived from the true covariance matrix. The uncertainty on the parameter combination $$\\Sigma_8 \\sim \\sigma_8 \\Omega_m^{0.5}$$ derived from internally estimated covariances is $$\\sim 90\\%$$ of the true uncertainty.« less

Galaxy-galaxy lensing estimators and their covariance properties

NASA Astrophysics Data System (ADS)

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uroš; Slosar, Anže; Vazquez Gonzalez, Jose

2017-11-01

We study the covariance properties of real space correlation function estimators - primarily galaxy-shear correlations, or galaxy-galaxy lensing - using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens density field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.

On the role of covariance information for GRACE K-band observations in the Celestial Mechanics Approach

NASA Astrophysics Data System (ADS)

Bentel, Katrin; Meyer, Ulrich; Arnold, Daniel; Jean, Yoomin; Jäggi, Adrian

2017-04-01

The Astronomical Institute at the University of Bern (AIUB) derives static and time-variable gravity fields by means of the Celestial Mechanics Approach (CMA) from GRACE (level 1B) data. This approach makes use of the close link between orbit and gravity field determination. GPS-derived kinematic GRACE orbit positions, inter-satellite K-band observations, which are the core observations of GRACE, and accelerometer data are combined to rigorously estimate orbit and spherical harmonic gravity field coefficients in one adjustment step. Pseudo-stochastic orbit parameters are set up to absorb unmodeled noise. The K-band range measurements in along-track direction lead to a much higher correlation of the observations in this direction compared to the other directions and thus, to north-south stripes in the unconstrained gravity field solutions, so-called correlated errors. By using a full covariance matrix for the K-band observations the correlation can be taken into account. One possibility is to derive correlation information from post-processing K-band residuals. This is then used in a second iteration step to derive an improved gravity field solution. We study the effects of pre-defined covariance matrices and residual-derived covariance matrices on the final gravity field product with the CMA.

On using summary statistics from an external calibration sample to correct for covariate measurement error.

PubMed

Guo, Ying; Little, Roderick J; McConnell, Daniel S

2012-01-01

Covariate measurement error is common in epidemiologic studies. Current methods for correcting measurement error with information from external calibration samples are insufficient to provide valid adjusted inferences. We consider the problem of estimating the regression of an outcome Y on covariates X and Z, where Y and Z are observed, X is unobserved, but a variable W that measures X with error is observed. Information about measurement error is provided in an external calibration sample where data on X and W (but not Y and Z) are recorded. We describe a method that uses summary statistics from the calibration sample to create multiple imputations of the missing values of X in the regression sample, so that the regression coefficients of Y on X and Z and associated standard errors can be estimated using simple multiple imputation combining rules, yielding valid statistical inferences under the assumption of a multivariate normal distribution. The proposed method is shown by simulation to provide better inferences than existing methods, namely the naive method, classical calibration, and regression calibration, particularly for correction for bias and achieving nominal confidence levels. We also illustrate our method with an example using linear regression to examine the relation between serum reproductive hormone concentrations and bone mineral density loss in midlife women in the Michigan Bone Health and Metabolism Study. Existing methods fail to adjust appropriately for bias due to measurement error in the regression setting, particularly when measurement error is substantial. The proposed method corrects this deficiency.

Empirical Likelihood in Nonignorable Covariate-Missing Data Problems.

PubMed

Xie, Yanmei; Zhang, Biao

2017-04-20

Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719-30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and

Lipid and Creatinine Adjustment to Evaluate Health Effects of Environmental Exposures.

PubMed

O'Brien, Katie M; Upson, Kristen; Buckley, Jessie P

2017-03-01

Urine- and serum-based biomarkers are useful for assessing individuals' exposure to environmental factors. However, variations in urinary creatinine (a measure of dilution) or serum lipid levels, if not adequately corrected for, can directly impact biomarker concentrations and bias exposure-disease association measures. Recent methodological literature has considered the complex relationships between creatinine or serum lipid levels, exposure biomarkers, outcomes, and other potentially relevant factors using directed acyclic graphs and simulation studies. The optimal measures of urinary dilution and serum lipids have also been investigated. Existing evidence supports the use of covariate-adjusted standardization plus creatinine adjustment for urinary biomarkers and standardization plus serum lipid adjustment for lipophilic, serum-based biomarkers. It is unclear which urinary dilution measure is best, but all serum lipid measures performed similarly. Future research should assess methods for pooled biomarkers and for studying diseases and exposures that affect creatinine or serum lipids directly.

Bayesian Nonparametric Ordination for the Analysis of Microbial Communities.

PubMed

Ren, Boyu; Bacallado, Sergio; Favaro, Stefano; Holmes, Susan; Trippa, Lorenzo

2017-01-01

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency tables with OTU counts across heterogeneous biological samples. In the microbial ecology community, ordination methods are frequently used to investigate latent factors or clusters that capture and describe variations of OTU counts across biological samples. It remains important to evaluate how uncertainty in estimates of each biological sample's microbial distribution propagates to ordination analyses, including visualization of clusters and projections of biological samples on low dimensional spaces. We propose a Bayesian analysis for dependent distributions to endow frequently used ordinations with estimates of uncertainty. A Bayesian nonparametric prior for dependent normalized random measures is constructed, which is marginally equivalent to the normalized generalized Gamma process, a well-known prior for nonparametric analyses. In our prior, the dependence and similarity between microbial distributions is represented by latent factors that concentrate in a low dimensional space. We use a shrinkage prior to tune the dimensionality of the latent factors. The resulting posterior samples of model parameters can be used to evaluate uncertainty in analyses routinely applied in microbiome studies. Specifically, by combining them with multivariate data analysis techniques we can visualize credible regions in ecological ordination plots. The characteristics of the proposed model are illustrated through a simulation study and applications in two microbiome datasets.

Nonparametric Analyses of Log-Periodic Precursors to Financial Crashes

NASA Astrophysics Data System (ADS)

Zhou, Wei-Xing; Sornette, Didier

We apply two nonparametric methods to further test the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The term "parametric" refers here to the use of the log-periodic power law formula to fit the data; in contrast, "nonparametric" refers to the use of general tools such as Fourier transform, and in the present case the Hilbert transform and the so-called (H, q)-analysis. The analysis using the (H, q)-derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln(tc-t) variable, where tc is the time of the crash. Taking all results together, we find strong evidence for a universal fundamental log-frequency f=1.02±0.05 corresponding to the scaling ratio λ=2.67±0.12. These values are in very good agreement with those obtained in earlier works with different parametric techniques. This note is extracted from a long unpublished report with 58 figures available at , which extensively describes the evidence we have accumulated on these seven time series, in particular by presenting all relevant details so that the reader can judge for himself or herself the validity and robustness of the results.

Multivariate analysis of covariates of adherence among HIV-positive mothers with low viral suppression.

PubMed

Nsubuga-Nyombi, Tamara; Sensalire, Simon; Karamagi, Esther; Aloyo, Judith; Byabagambi, John; Rahimzai, Mirwais; Nabitaka, Linda Kisaakye; Calnan, Jacqueline

2018-03-31

As part of efforts to improve the prevention of mother-to-child transmission in Northern Uganda, we explored reasons for poor viral suppression among 122 pregnant and lactating women who were in care, received viral load tests, but had not achieved viral suppression and had more than 1000 copies/mL. Understanding the patient factors associated with low viral suppression was of interest to the Ministry of Health to guide the development of tools and interventions to achieve viral suppression for pregnant and lactating women newly initiating on ART as well as those on ART with unsuppressed viral load. A facility-based cross-sectional and mixed methods study design was used, with retrospective medical record review. We assessed 122 HIV-positive mothers with known low viral suppression across 31 health facilities in Northern Uganda. Adjusted odds ratios were used to determine the covariates of adherence among HIV positive mothers using logistic regression. A study among health care providers shed further light on predictors of low viral suppression and a history of low early retention. This study was part of a larger national evaluation of the performance of integrated care services for mothers. Adherence defined as taking antiretroviral medications correctly everyday was low at 67.2%. The covariates of low adherence are: taking other medications in addition to ART, missed appointments in the past 6 months, experienced violence in the past 6 months, and faces obstacles to treatment. Mothers who were experiencing each of these covariates were less likely to adhere to treatment. These covariates were triangulated with perspectives of health providers as covariates of low adherence and included: long distances to health facility, missed appointments, running out of pills, sharing antiretroviral drugs, violence, and social lifestyles such as multiple sexual partners coupled with non-disclosure to partners. Inadequate counseling, stigma, and lack of client identity are

Large Covariance Estimation by Thresholding Principal Orthogonal Complements

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented. PMID:24348088

Alterations in Anatomical Covariance in the Prematurely Born

PubMed Central

Scheinost, Dustin; Kwon, Soo Hyun; Lacadie, Cheryl; Vohr, Betty R.; Schneider, Karen C.; Papademetris, Xenophon; Constable, R. Todd; Ment, Laura R.

2017-01-01

Abstract Preterm (PT) birth results in long-term alterations in functional and structural connectivity, but the related changes in anatomical covariance are just beginning to be explored. To test the hypothesis that PT birth alters patterns of anatomical covariance, we investigated brain volumes of 25 PTs and 22 terms at young adulthood using magnetic resonance imaging. Using regional volumetrics, seed-based analyses, and whole brain graphs, we show that PT birth is associated with reduced volume in bilateral temporal and inferior frontal lobes, left caudate, left fusiform, and posterior cingulate for prematurely born subjects at young adulthood. Seed-based analyses demonstrate altered patterns of anatomical covariance for PTs compared with terms. PTs exhibit reduced covariance with R Brodmann area (BA) 47, Broca's area, and L BA 21, Wernicke's area, and white matter volume in the left prefrontal lobe, but increased covariance with R BA 47 and left cerebellum. Graph theory analyses demonstrate that measures of network complexity are significantly less robust in PTs compared with term controls. Volumes in regions showing group differences are significantly correlated with phonological awareness, the fundamental basis for reading acquisition, for the PTs. These data suggest both long-lasting and clinically significant alterations in the covariance in the PTs at young adulthood. PMID:26494796

Hyperspectral image segmentation using a cooperative nonparametric approach

NASA Astrophysics Data System (ADS)

Taher, Akar; Chehdi, Kacem; Cariou, Claude

2013-10-01

In this paper a new unsupervised nonparametric cooperative and adaptive hyperspectral image segmentation approach is presented. The hyperspectral images are partitioned band by band in parallel and intermediate classification results are evaluated and fused, to get the final segmentation result. Two unsupervised nonparametric segmentation methods are used in parallel cooperation, namely the Fuzzy C-means (FCM) method, and the Linde-Buzo-Gray (LBG) algorithm, to segment each band of the image. The originality of the approach relies firstly on its local adaptation to the type of regions in an image (textured, non-textured), and secondly on the introduction of several levels of evaluation and validation of intermediate segmentation results before obtaining the final partitioning of the image. For the management of similar or conflicting results issued from the two classification methods, we gradually introduced various assessment steps that exploit the information of each spectral band and its adjacent bands, and finally the information of all the spectral bands. In our approach, the detected textured and non-textured regions are treated separately from feature extraction step, up to the final classification results. This approach was first evaluated on a large number of monocomponent images constructed from the Brodatz album. Then it was evaluated on two real applications using a respectively multispectral image for Cedar trees detection in the region of Baabdat (Lebanon) and a hyperspectral image for identification of invasive and non invasive vegetation in the region of Cieza (Spain). A correct classification rate (CCR) for the first application is over 97% and for the second application the average correct classification rate (ACCR) is over 99%.

A framework for multivariate data-based at-site flood frequency analysis: Essentiality of the conjugal application of parametric and nonparametric approaches

NASA Astrophysics Data System (ADS)

Vittal, H.; Singh, Jitendra; Kumar, Pankaj; Karmakar, Subhankar

2015-06-01

In watershed management, flood frequency analysis (FFA) is performed to quantify the risk of flooding at different spatial locations and also to provide guidelines for determining the design periods of flood control structures. The traditional FFA was extensively performed by considering univariate scenario for both at-site and regional estimation of return periods. However, due to inherent mutual dependence of the flood variables or characteristics [i.e., peak flow (P), flood volume (V) and flood duration (D), which are random in nature], analysis has been further extended to multivariate scenario, with some restrictive assumptions. To overcome the assumption of same family of marginal density function for all flood variables, the concept of copula has been introduced. Although, the advancement from univariate to multivariate analyses drew formidable attention to the FFA research community, the basic limitation was that the analyses were performed with the implementation of only parametric family of distributions. The aim of the current study is to emphasize the importance of nonparametric approaches in the field of multivariate FFA; however, the nonparametric distribution may not always be a good-fit and capable of replacing well-implemented multivariate parametric and multivariate copula-based applications. Nevertheless, the potential of obtaining best-fit using nonparametric distributions might be improved because such distributions reproduce the sample's characteristics, resulting in more accurate estimations of the multivariate return period. Hence, the current study shows the importance of conjugating multivariate nonparametric approach with multivariate parametric and copula-based approaches, thereby results in a comprehensive framework for complete at-site FFA. Although the proposed framework is designed for at-site FFA, this approach can also be applied to regional FFA because regional estimations ideally include at-site estimations. The framework is

Testing the Hypothesis of a Homoscedastic Error Term in Simple, Nonparametric Regression

ERIC Educational Resources Information Center

Wilcox, Rand R.

2006-01-01

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

How to Compare Parametric and Nonparametric Person-Fit Statistics Using Real Data

ERIC Educational Resources Information Center

Sinharay, Sandip

2017-01-01

Person-fit assessment (PFA) is concerned with uncovering atypical test performance as reflected in the pattern of scores on individual items on a test. Existing person-fit statistics (PFSs) include both parametric and nonparametric statistics. Comparison of PFSs has been a popular research topic in PFA, but almost all comparisons have employed…

The Role of Executive Functions Skills and Self-Regulation Behaviors in School Readiness and Adjustment

ERIC Educational Resources Information Center

Sasser, Tyler R.; Bierman, Karen L.

2012-01-01

The aim of this study was to examine co-variation in the development of self-regulatory skills evident in pre-kindergarten and evaluate the implications of that variation for school adjustment in kindergarten and first grade. Measures of self-regulatory skill development included: direct assessments of EF (executive function) (e.g., Peg Tapping,…

Galaxy–galaxy lensing estimators and their covariance properties

DOE PAGES

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uros; ...

2017-07-21

Here, we study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens densitymore » field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.« less

Galaxy–galaxy lensing estimators and their covariance properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Sukhdeep; Mandelbaum, Rachel; Seljak, Uros

Here, we study the covariance properties of real space correlation function estimators – primarily galaxy–shear correlations, or galaxy–galaxy lensing – using SDSS data for both shear catalogues and lenses (specifically the BOSS LOWZ sample). Using mock catalogues of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the lens overdensity field. While the measurement using the lens densitymore » field is unbiased (in the absence of systematics), its error is significantly larger due to an additional term in the covariance. Therefore, this subtraction should be performed regardless of its beneficial effects on systematics. Comparing the error estimates from data and mocks for estimators that involve the overdensity, we find that the errors are dominated by the shape noise and lens clustering, which empirically estimated covariances (jackknife and standard deviation across mocks) that are consistent with theoretical estimates, and that both the connected parts of the four-point function and the supersample covariance can be neglected for the current levels of noise. While the trade-off between different terms in the covariance depends on the survey configuration (area, source number density), the diagnostics that we use in this work should be useful for future works to test their empirically determined covariances.« less

Short-term forecasting of meteorological time series using Nonparametric Functional Data Analysis (NPFDA)

NASA Astrophysics Data System (ADS)

Curceac, S.; Ternynck, C.; Ouarda, T.

2015-12-01

Over the past decades, a substantial amount of research has been conducted to model and forecast climatic variables. In this study, Nonparametric Functional Data Analysis (NPFDA) methods are applied to forecast air temperature and wind speed time series in Abu Dhabi, UAE. The dataset consists of hourly measurements recorded for a period of 29 years, 1982-2010. The novelty of the Functional Data Analysis approach is in expressing the data as curves. In the present work, the focus is on daily forecasting and the functional observations (curves) express the daily measurements of the above mentioned variables. We apply a non-linear regression model with a functional non-parametric kernel estimator. The computation of the estimator is performed using an asymmetrical quadratic kernel function for local weighting based on the bandwidth obtained by a cross validation procedure. The proximities between functional objects are calculated by families of semi-metrics based on derivatives and Functional Principal Component Analysis (FPCA). Additionally, functional conditional mode and functional conditional median estimators are applied and the advantages of combining their results are analysed. A different approach employs a SARIMA model selected according to the minimum Akaike (AIC) and Bayessian (BIC) Information Criteria and based on the residuals of the model. The performance of the models is assessed by calculating error indices such as the root mean square error (RMSE), relative RMSE, BIAS and relative BIAS. The results indicate that the NPFDA models provide more accurate forecasts than the SARIMA models. Key words: Nonparametric functional data analysis, SARIMA, time series forecast, air temperature, wind speed

On the Bias-Amplifying Effect of Near Instruments in Observational Studies

ERIC Educational Resources Information Center

Steiner, Peter M.; Kim, Yongnam

2014-01-01

In contrast to randomized experiments, the estimation of unbiased treatment effects from observational data requires an analysis that conditions on all confounding covariates. Conditioning on covariates can be done via standard parametric regression techniques or nonparametric matching like propensity score (PS) matching. The regression or…

A multi-instrument non-parametric reconstruction of the electron pressure profile in the galaxy cluster CLJ1226.9+3332

NASA Astrophysics Data System (ADS)

Romero, C.; McWilliam, M.; Macías-Pérez, J.-F.; Adam, R.; Ade, P.; André, P.; Aussel, H.; Beelen, A.; Benoît, A.; Bideaud, A.; Billot, N.; Bourrion, O.; Calvo, M.; Catalano, A.; Coiffard, G.; Comis, B.; de Petris, M.; Désert, F.-X.; Doyle, S.; Goupy, J.; Kramer, C.; Lagache, G.; Leclercq, S.; Lestrade, J.-F.; Mauskopf, P.; Mayet, F.; Monfardini, A.; Pascale, E.; Perotto, L.; Pisano, G.; Ponthieu, N.; Revéret, V.; Ritacco, A.; Roussel, H.; Ruppin, F.; Schuster, K.; Sievers, A.; Triqueneaux, S.; Tucker, C.; Zylka, R.

2018-04-01

Context. In the past decade, sensitive, resolved Sunyaev-Zel'dovich (SZ) studies of galaxy clusters have become common. Whereas many previous SZ studies have parameterized the pressure profiles of galaxy clusters, non-parametric reconstructions will provide insights into the thermodynamic state of the intracluster medium. Aim. We seek to recover the non-parametric pressure profiles of the high redshift (z = 0.89) galaxy cluster CLJ 1226.9+3332 as inferred from SZ data from the MUSTANG, NIKA, Bolocam, and Planck instruments, which all probe different angular scales. Methods: Our non-parametric algorithm makes use of logarithmic interpolation, which under the assumption of ellipsoidal symmetry is analytically integrable. For MUSTANG, NIKA, and Bolocam we derive a non-parametric pressure profile independently and find good agreement among the instruments. In particular, we find that the non-parametric profiles are consistent with a fitted generalized Navaro-Frenk-White (gNFW) profile. Given the ability of Planck to constrain the total signal, we include a prior on the integrated Compton Y parameter as determined by Planck. Results: For a given instrument, constraints on the pressure profile diminish rapidly beyond the field of view. The overlap in spatial scales probed by these four datasets is therefore critical in checking for consistency between instruments. By using multiple instruments, our analysis of CLJ 1226.9+3332 covers a large radial range, from the central regions to the cluster outskirts: 0.05 R500 < r < 1.1 R500. This is a wider range of spatial scales than is typically recovered by SZ instruments. Similar analyses will be possible with the new generation of SZ instruments such as NIKA2 and MUSTANG2.

Nonrelativistic fluids on scale covariant Newton-Cartan backgrounds

NASA Astrophysics Data System (ADS)

Mitra, Arpita

2017-12-01

The nonrelativistic covariant framework for fields is extended to investigate fields and fluids on scale covariant curved backgrounds. The scale covariant Newton-Cartan background is constructed using the localization of space-time symmetries of nonrelativistic fields in flat space. Following this, we provide a Weyl covariant formalism which can be used to study scale invariant fluids. By considering ideal fluids as an example, we describe its thermodynamic and hydrodynamic properties and explicitly demonstrate that it satisfies the local second law of thermodynamics. As a further application, we consider the low energy description of Hall fluids. Specifically, we find that the gauge fields for scale transformations lead to corrections of the Wen-Zee and Berry phase terms contained in the effective action.

Empirical State Error Covariance Matrix for Batch Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joe

2015-01-01

State estimation techniques effectively provide mean state estimates. However, the theoretical state error covariance matrices provided as part of these techniques often suffer from a lack of confidence in their ability to describe the uncertainty in the estimated states. By a reinterpretation of the equations involved in the weighted batch least squares algorithm, it is possible to directly arrive at an empirical state error covariance matrix. The proposed empirical state error covariance matrix will contain the effect of all error sources, known or not. This empirical error covariance matrix may be calculated as a side computation for each unique batch solution. Results based on the proposed technique will be presented for a simple, two observer and measurement error only problem.

Hidden Covariation Detection Produces Faster, Not Slower, Social Judgments

ERIC Educational Resources Information Center

Barker, Lynne A.; Andrade, Jackie

2006-01-01

In P. Lewicki's (1986b) demonstration of hidden covariation detection (HCD), responses of participants were slower to faces that corresponded with a covariation encountered previously than to faces with novel covariations. This slowing contrasts with the typical finding that priming leads to faster responding and suggests that HCD is a unique type…

Nonparametric and Semiparametric Regression Estimation for Length-biased Survival Data

PubMed Central

Shen, Yu; Ning, Jing; Qin, Jing

2016-01-01

For the past several decades, nonparametric and semiparametric modeling for conventional right-censored survival data has been investigated intensively under a noninformative censoring mechanism. However, these methods may not be applicable for analyzing right-censored survival data that arise from prevalent cohorts when the failure times are subject to length-biased sampling. This review article is intended to provide a summary of some newly developed methods as well as established methods for analyzing length-biased data. PMID:27086362

Optimum nonparametric estimation of population density based on ordered distances

USGS Publications Warehouse

Patil, S.A.; Kovner, J.L.; Burnham, Kenneth P.

1982-01-01

The asymptotic mean and error mean square are determined for the nonparametric estimator of plant density by distance sampling proposed by Patil, Burnham and Kovner (1979, Biometrics 35, 597-604. On the basis of these formulae, a bias-reduced version of this estimator is given, and its specific form is determined which gives minimum mean square error under varying assumptions about the true probability density function of the sampled data. Extension is given to line-transect sampling.

Bayes Factor Covariance Testing in Item Response Models.

PubMed

Fox, Jean-Paul; Mulder, Joris; Sinharay, Sandip

2017-12-01

Two marginal one-parameter item response theory models are introduced, by integrating out the latent variable or random item parameter. It is shown that both marginal response models are multivariate (probit) models with a compound symmetry covariance structure. Several common hypotheses concerning the underlying covariance structure are evaluated using (fractional) Bayes factor tests. The support for a unidimensional factor (i.e., assumption of local independence) and differential item functioning are evaluated by testing the covariance components. The posterior distribution of common covariance components is obtained in closed form by transforming latent responses with an orthogonal (Helmert) matrix. This posterior distribution is defined as a shifted-inverse-gamma, thereby introducing a default prior and a balanced prior distribution. Based on that, an MCMC algorithm is described to estimate all model parameters and to compute (fractional) Bayes factor tests. Simulation studies are used to show that the (fractional) Bayes factor tests have good properties for testing the underlying covariance structure of binary response data. The method is illustrated with two real data studies.

Alterations in Anatomical Covariance in the Prematurely Born.

PubMed

Scheinost, Dustin; Kwon, Soo Hyun; Lacadie, Cheryl; Vohr, Betty R; Schneider, Karen C; Papademetris, Xenophon; Constable, R Todd; Ment, Laura R

2017-01-01

Preterm (PT) birth results in long-term alterations in functional and structural connectivity, but the related changes in anatomical covariance are just beginning to be explored. To test the hypothesis that PT birth alters patterns of anatomical covariance, we investigated brain volumes of 25 PTs and 22 terms at young adulthood using magnetic resonance imaging. Using regional volumetrics, seed-based analyses, and whole brain graphs, we show that PT birth is associated with reduced volume in bilateral temporal and inferior frontal lobes, left caudate, left fusiform, and posterior cingulate for prematurely born subjects at young adulthood. Seed-based analyses demonstrate altered patterns of anatomical covariance for PTs compared with terms. PTs exhibit reduced covariance with R Brodmann area (BA) 47, Broca's area, and L BA 21, Wernicke's area, and white matter volume in the left prefrontal lobe, but increased covariance with R BA 47 and left cerebellum. Graph theory analyses demonstrate that measures of network complexity are significantly less robust in PTs compared with term controls. Volumes in regions showing group differences are significantly correlated with phonological awareness, the fundamental basis for reading acquisition, for the PTs. These data suggest both long-lasting and clinically significant alterations in the covariance in the PTs at young adulthood. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Massive data compression for parameter-dependent covariance matrices

NASA Astrophysics Data System (ADS)

Heavens, Alan F.; Sellentin, Elena; de Mijolla, Damien; Vianello, Alvise

2017-12-01

We show how the massive data compression algorithm MOPED can be used to reduce, by orders of magnitude, the number of simulated data sets which are required to estimate the covariance matrix required for the analysis of Gaussian-distributed data. This is relevant when the covariance matrix cannot be calculated directly. The compression is especially valuable when the covariance matrix varies with the model parameters. In this case, it may be prohibitively expensive to run enough simulations to estimate the full covariance matrix throughout the parameter space. This compression may be particularly valuable for the next generation of weak lensing surveys, such as proposed for Euclid and Large Synoptic Survey Telescope, for which the number of summary data (such as band power or shear correlation estimates) is very large, ∼104, due to the large number of tomographic redshift bins which the data will be divided into. In the pessimistic case where the covariance matrix is estimated separately for all points in an Monte Carlo Markov Chain analysis, this may require an unfeasible 109 simulations. We show here that MOPED can reduce this number by a factor of 1000, or a factor of ∼106 if some regularity in the covariance matrix is assumed, reducing the number of simulations required to a manageable 103, making an otherwise intractable analysis feasible.

Hawking radiation, covariant boundary conditions, and vacuum states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Rabin; Kulkarni, Shailesh

2009-04-15

The basic characteristics of the covariant chiral current and the covariant chiral energy-momentum tensor are obtained from a chiral effective action. These results are used to justify the covariant boundary condition used in recent approaches of computing the Hawking flux from chiral gauge and gravitational anomalies. We also discuss a connection of our results with the conventional calculation of nonchiral currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware) states.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2011-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Modeling spatiotemporal covariance for magnetoencephalography or electroencephalography source analysis.

PubMed

Plis, Sergey M; George, J S; Jun, S C; Paré-Blagoev, J; Ranken, D M; Wood, C C; Schmidt, D M

2007-01-01

We propose a new model to approximate spatiotemporal noise covariance for use in neural electromagnetic source analysis, which better captures temporal variability in background activity. As with other existing formalisms, our model employs a Kronecker product of matrices representing temporal and spatial covariance. In our model, spatial components are allowed to have differing temporal covariances. Variability is represented as a series of Kronecker products of spatial component covariances and corresponding temporal covariances. Unlike previous attempts to model covariance through a sum of Kronecker products, our model is designed to have a computationally manageable inverse. Despite increased descriptive power, inversion of the model is fast, making it useful in source analysis. We have explored two versions of the model. One is estimated based on the assumption that spatial components of background noise have uncorrelated time courses. Another version, which gives closer approximation, is based on the assumption that time courses are statistically independent. The accuracy of the structural approximation is compared to an existing model, based on a single Kronecker product, using both Frobenius norm of the difference between spatiotemporal sample covariance and a model, and scatter plots. Performance of ours and previous models is compared in source analysis of a large number of single dipole problems with simulated time courses and with background from authentic magnetoencephalography data.

Does Maternal HIV Disclosure Self-Efficacy Enhance Parent-Child Relationships and Child Adjustment?

PubMed

Armistead, Lisa; Goodrum, Nada; Schulte, Marya; Marelich, William; LeCroix, Rebecca; Murphy, Debra A

2018-02-09

Nondisclosure of maternal HIV status to young children can negatively impact child functioning; however, many mothers do not disclose due to lack of self-efficacy for the disclosure process. This study examines demographic variations in disclosure self-efficacy, regardless of intention to disclose, and assesses the relationship between self-efficacy and child adjustment via the parent-child relationship among a sample of HIV+ mothers and their healthy children (N = 181 pairs). Mothers completed demographic and self-efficacy measures; children completed measures assessing the parent-child relationship and child adjustment (i.e., worry, self-concept, depression). Across demographics, few mothers reported confidence in disclosure. Results from covariance structural modeling showed mothers endorsing higher self-efficacy had children who reported better relationship quality, and, in turn, reported fewer adjustment difficulties; higher levels of disclosure self-efficacy also directly predicted fewer adjustment problems. Findings offer support for interventions aimed at providing mothers with skills to enhance confidence for disclosing their HIV status.

Lipid and Creatinine Adjustment to Evaluate Health Effects of Environmental Exposures

PubMed Central

O’Brien, Katie M.; Upson, Kristen; Buckley, Jessie P.

2017-01-01

Purpose of review Urine- and serum-based biomarkers are useful for assessing individuals’ exposure to environmental factors. However, variations in urinary creatinine (a measure of dilution) or serum lipid levels, if not adequately corrected for, can directly impact biomarker concentrations and bias exposure-disease association measures. Recent findings Recent methodological literature has considered the complex relationships between creatinine or serum lipid levels, exposure biomarkers, outcomes, and other potentially relevant factors using directed acyclic graphs and simulation studies. The optimal measures of urinary dilution and serum lipids have also been investigated. Summary Existing evidence supports the use of covariate-adjusted standardization plus creatinine adjustment for urinary biomarkers and standardization plus serum lipid adjustment for lipophilic, serum-based biomarkers. It is unclear which urinary dilution measure is best, but all serum lipid measures performed similarly. Future research should assess methods for pooled biomarkers and for studying diseases and exposures that affect creatinine or serum lipids directly. PMID:28097619

Remediating Non-Positive Definite State Covariances for Collision Probability Estimation

NASA Technical Reports Server (NTRS)

Hall, Doyle T.; Hejduk, Matthew D.; Johnson, Lauren C.

2017-01-01

The NASA Conjunction Assessment Risk Analysis team estimates the probability of collision (Pc) for a set of Earth-orbiting satellites. The Pc estimation software processes satellite position+velocity states and their associated covariance matri-ces. On occasion, the software encounters non-positive definite (NPD) state co-variances, which can adversely affect or prevent the Pc estimation process. Inter-polation inaccuracies appear to account for the majority of such covariances, alt-hough other mechanisms contribute also. This paper investigates the origin of NPD state covariance matrices, three different methods for remediating these co-variances when and if necessary, and the associated effects on the Pc estimation process.

Frame covariant nonminimal multifield inflation

NASA Astrophysics Data System (ADS)

Karamitsos, Sotirios; Pilaftsis, Apostolos

2018-02-01

We introduce a frame-covariant formalism for inflation of scalar-curvature theories by adopting a differential geometric approach which treats the scalar fields as coordinates living on a field-space manifold. This ensures that our description of inflation is both conformally and reparameterization covariant. Our formulation gives rise to extensions of the usual Hubble and potential slow-roll parameters to generalized fully frame-covariant forms, which allow us to provide manifestly frame-invariant predictions for cosmological observables, such as the tensor-to-scalar ratio r, the spectral indices nR and nT, their runnings αR and αT, the non-Gaussianity parameter fNL, and the isocurvature fraction βiso. We examine the role of the field space curvature in the generation and transfer of isocurvature modes, and we investigate the effect of boundary conditions for the scalar fields at the end of inflation on the observable inflationary quantities. We explore the stability of the trajectories with respect to the boundary conditions by using a suitable sensitivity parameter. To illustrate our approach, we first analyze a simple minimal two-field scenario before studying a more realistic nonminimal model inspired by Higgs inflation. We find that isocurvature effects are greatly enhanced in the latter scenario and must be taken into account for certain values in the parameter space such that the model is properly normalized to the observed scalar power spectrum PR. Finally, we outline how our frame-covariant approach may be extended beyond the tree-level approximation through the Vilkovisky-De Witt formalism, which we generalize to take into account conformal transformations, thereby leading to a fully frame-invariant effective action at the one-loop level.

DISSCO: direct imputation of summary statistics allowing covariates

PubMed Central

Xu, Zheng; Duan, Qing; Yan, Song; Chen, Wei; Li, Mingyao; Lange, Ethan; Li, Yun

2015-01-01

Background: Imputation of individual level genotypes at untyped markers using an external reference panel of genotyped or sequenced individuals has become standard practice in genetic association studies. Direct imputation of summary statistics can also be valuable, for example in meta-analyses where individual level genotype data are not available. Two methods (DIST and ImpG-Summary/LD), that assume a multivariate Gaussian distribution for the association summary statistics, have been proposed for imputing association summary statistics. However, both methods assume that the correlations between association summary statistics are the same as the correlations between the corresponding genotypes. This assumption can be violated in the presence of confounding covariates. Methods: We analytically show that in the absence of covariates, correlation among association summary statistics is indeed the same as that among the corresponding genotypes, thus serving as a theoretical justification for the recently proposed methods. We continue to prove that in the presence of covariates, correlation among association summary statistics becomes the partial correlation of the corresponding genotypes controlling for covariates. We therefore develop direct imputation of summary statistics allowing covariates (DISSCO). Results: We consider two real-life scenarios where the correlation and partial correlation likely make practical difference: (i) association studies in admixed populations; (ii) association studies in presence of other confounding covariate(s). Application of DISSCO to real datasets under both scenarios shows at least comparable, if not better, performance compared with existing correlation-based methods, particularly for lower frequency variants. For example, DISSCO can reduce the absolute deviation from the truth by 3.9–15.2% for variants with minor allele frequency <5%. Availability and implementation: http://www.unc.edu/∼yunmli/DISSCO. Contact: yunli

DISSCO: direct imputation of summary statistics allowing covariates.

PubMed

Xu, Zheng; Duan, Qing; Yan, Song; Chen, Wei; Li, Mingyao; Lange, Ethan; Li, Yun

2015-08-01

Imputation of individual level genotypes at untyped markers using an external reference panel of genotyped or sequenced individuals has become standard practice in genetic association studies. Direct imputation of summary statistics can also be valuable, for example in meta-analyses where individual level genotype data are not available. Two methods (DIST and ImpG-Summary/LD), that assume a multivariate Gaussian distribution for the association summary statistics, have been proposed for imputing association summary statistics. However, both methods assume that the correlations between association summary statistics are the same as the correlations between the corresponding genotypes. This assumption can be violated in the presence of confounding covariates. We analytically show that in the absence of covariates, correlation among association summary statistics is indeed the same as that among the corresponding genotypes, thus serving as a theoretical justification for the recently proposed methods. We continue to prove that in the presence of covariates, correlation among association summary statistics becomes the partial correlation of the corresponding genotypes controlling for covariates. We therefore develop direct imputation of summary statistics allowing covariates (DISSCO). We consider two real-life scenarios where the correlation and partial correlation likely make practical difference: (i) association studies in admixed populations; (ii) association studies in presence of other confounding covariate(s). Application of DISSCO to real datasets under both scenarios shows at least comparable, if not better, performance compared with existing correlation-based methods, particularly for lower frequency variants. For example, DISSCO can reduce the absolute deviation from the truth by 3.9-15.2% for variants with minor allele frequency <5%. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Real-time probabilistic covariance tracking with efficient model update.

PubMed

Wu, Yi; Cheng, Jian; Wang, Jinqiao; Lu, Hanqing; Wang, Jun; Ling, Haibin; Blasch, Erik; Bai, Li

2012-05-01

The recently proposed covariance region descriptor has been proven robust and versatile for a modest computational cost. The covariance matrix enables efficient fusion of different types of features, where the spatial and statistical properties, as well as their correlation, are characterized. The similarity between two covariance descriptors is measured on Riemannian manifolds. Based on the same metric but with a probabilistic framework, we propose a novel tracking approach on Riemannian manifolds with a novel incremental covariance tensor learning (ICTL). To address the appearance variations, ICTL incrementally learns a low-dimensional covariance tensor representation and efficiently adapts online to appearance changes of the target with only O(1) computational complexity, resulting in a real-time performance. The covariance-based representation and the ICTL are then combined with the particle filter framework to allow better handling of background clutter, as well as the temporary occlusions. We test the proposed probabilistic ICTL tracker on numerous benchmark sequences involving different types of challenges including occlusions and variations in illumination, scale, and pose. The proposed approach demonstrates excellent real-time performance, both qualitatively and quantitatively, in comparison with several previously proposed trackers.

A three domain covariance framework for EEG/MEG data.

PubMed

Roś, Beata P; Bijma, Fetsje; de Gunst, Mathisca C M; de Munck, Jan C

2015-10-01

In this paper we introduce a covariance framework for the analysis of single subject EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. Our covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, like in combined EEG-fMRI experiments in which the correlation between EEG and fMRI signals is investigated. We use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. We apply our method to real EEG and MEG data sets. Copyright © 2015 Elsevier Inc. All rights reserved.

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied. PMID:22661790

Multiple feature fusion via covariance matrix for visual tracking

NASA Astrophysics Data System (ADS)

Jin, Zefenfen; Hou, Zhiqiang; Yu, Wangsheng; Wang, Xin; Sun, Hui

2018-04-01

Aiming at the problem of complicated dynamic scenes in visual target tracking, a multi-feature fusion tracking algorithm based on covariance matrix is proposed to improve the robustness of the tracking algorithm. In the frame-work of quantum genetic algorithm, this paper uses the region covariance descriptor to fuse the color, edge and texture features. It also uses a fast covariance intersection algorithm to update the model. The low dimension of region covariance descriptor, the fast convergence speed and strong global optimization ability of quantum genetic algorithm, and the fast computation of fast covariance intersection algorithm are used to improve the computational efficiency of fusion, matching, and updating process, so that the algorithm achieves a fast and effective multi-feature fusion tracking. The experiments prove that the proposed algorithm can not only achieve fast and robust tracking but also effectively handle interference of occlusion, rotation, deformation, motion blur and so on.

Covariance Matrix Evaluations for Independent Mass Fission Yields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Terranova, N., E-mail: nicholas.terranova@unibo.it; Serot, O.; Archier, P.

2015-01-15

Recent needs for more accurate fission product yields include covariance information to allow improved uncertainty estimations of the parameters used by design codes. The aim of this work is to investigate the possibility to generate more reliable and complete uncertainty information on independent mass fission yields. Mass yields covariances are estimated through a convolution between the multi-Gaussian empirical model based on Brosa's fission modes, which describe the pre-neutron mass yields, and the average prompt neutron multiplicity curve. The covariance generation task has been approached using the Bayesian generalized least squared method through the CONRAD code. Preliminary results on mass yieldsmore » variance-covariance matrix will be presented and discussed from physical grounds in the case of {sup 235}U(n{sub th}, f) and {sup 239}Pu(n{sub th}, f) reactions.« less

True covariance simulation of the EUVE update filter

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Harman, R. R.

1989-01-01

A covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the On Board Computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft is presented. The linearized dynamics and measurement equations of the error states are derived which constitute the truth model describing the real behavior of the systems involved. The design model used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A true covariance analysis has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Development and Validation of Perioperative Risk-Adjustment Models for Hip Fracture Repair, Total Hip Arthroplasty, and Total Knee Arthroplasty.

PubMed

Schilling, Peter L; Bozic, Kevin J

2016-01-06

Comparing outcomes across providers requires risk-adjustment models that account for differences in case mix. The burden of data collection from the clinical record can make risk-adjusted outcomes difficult to measure. The purpose of this study was to develop risk-adjustment models for hip fracture repair (HFR), total hip arthroplasty (THA), and total knee arthroplasty (TKA) that weigh adequacy of risk adjustment against data-collection burden. We used data from the American College of Surgeons National Surgical Quality Improvement Program to create derivation cohorts for HFR (n = 7000), THA (n = 17,336), and TKA (n = 28,661). We developed logistic regression models for each procedure using age, sex, American Society of Anesthesiologists (ASA) physical status classification, comorbidities, laboratory values, and vital signs-based comorbidities as covariates, and validated the models with use of data from 2012. The derivation models' C-statistics for mortality were 80%, 81%, 75%, and 92% and for adverse events were 68%, 68%, 60%, and 70% for HFR, THA, TKA, and combined procedure cohorts. Age, sex, and ASA classification accounted for a large share of the explained variation in mortality (50%, 58%, 70%, and 67%) and adverse events (43%, 45%, 46%, and 68%). For THA and TKA, these three variables were nearly as predictive as models utilizing all covariates. HFR model discrimination improved with the addition of comorbidities and laboratory values; among the important covariates were functional status, low albumin, high creatinine, disseminated cancer, dyspnea, and body mass index. Model performance was similar in validation cohorts. Risk-adjustment models using data from health records demonstrated good discrimination and calibration for HFR, THA, and TKA. It is possible to provide adequate risk adjustment using only the most predictive variables commonly available within the clinical record. This finding helps to inform the trade-off between model performance and data

A Bayesian Semiparametric Latent Variable Model for Mixed Responses

ERIC Educational Resources Information Center

Fahrmeir, Ludwig; Raach, Alexander

2007-01-01

In this paper we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric Gaussian regression model. We extend existing LVMs with the usual linear covariate effects by including nonparametric components for nonlinear…

Bayesian hierarchical model for large-scale covariance matrix estimation.

PubMed

Zhu, Dongxiao; Hero, Alfred O

2007-12-01

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.

Does Private Tutoring Work? The Effectiveness of Private Tutoring: A Nonparametric Bounds Analysis

ERIC Educational Resources Information Center

Hof, Stefanie

2014-01-01

Private tutoring has become popular throughout the world. However, evidence for the effect of private tutoring on students' academic outcome is inconclusive; therefore, this paper presents an alternative framework: a nonparametric bounds method. The present examination uses, for the first time, a large representative data-set in a European setting…

A Note on the Assumption of Identical Distributions for Nonparametric Tests of Location

ERIC Educational Resources Information Center

Nordstokke, David W.; Colp, S. Mitchell

2018-01-01

Often, when testing for shift in location, researchers will utilize nonparametric statistical tests in place of their parametric counterparts when there is evidence or belief that the assumptions of the parametric test are not met (i.e., normally distributed dependent variables). An underlying and often unattended to assumption of nonparametric…

A Comparative Study of Test Data Dimensionality Assessment Procedures Under Nonparametric IRT Models

ERIC Educational Resources Information Center

van Abswoude, Alexandra A. H.; van der Ark, L. Andries; Sijtsma, Klaas

2004-01-01

In this article, an overview of nonparametric item response theory methods for determining the dimensionality of item response data is provided. Four methods were considered: MSP, DETECT, HCA/CCPROX, and DIMTEST. First, the methods were compared theoretically. Second, a simulation study was done to compare the effectiveness of MSP, DETECT, and…

Perturbative approach to covariance matrix of the matter power spectrum

NASA Astrophysics Data System (ADS)

Mohammed, Irshad; Seljak, Uroš; Vlah, Zvonimir

2017-04-01

We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (supersample variance) and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10 per cent level up to k ˜ 1 h Mpc-1. We show that all the connected components are dominated by the large-scale modes (k < 0.1 h Mpc-1), regardless of the value of the wave vectors k, k΄ of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher k, it is dominated by a single eigenmode. The full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally, we provide a prescription for how to evaluate the covariance matrix from small box simulations without the need to simulate large volumes.

Cox model with interval-censored covariate in cohort studies.

PubMed

Ahn, Soohyun; Lim, Johan; Paik, Myunghee Cho; Sacco, Ralph L; Elkind, Mitchell S

2018-05-18

In cohort studies the outcome is often time to a particular event, and subjects are followed at regular intervals. Periodic visits may also monitor a secondary irreversible event influencing the event of primary interest, and a significant proportion of subjects develop the secondary event over the period of follow-up. The status of the secondary event serves as a time-varying covariate, but is recorded only at the times of the scheduled visits, generating incomplete time-varying covariates. While information on a typical time-varying covariate is missing for entire follow-up period except the visiting times, the status of the secondary event are unavailable only between visits where the status has changed, thus interval-censored. One may view interval-censored covariate of the secondary event status as missing time-varying covariates, yet missingness is partial since partial information is provided throughout the follow-up period. Current practice of using the latest observed status produces biased estimators, and the existing missing covariate techniques cannot accommodate the special feature of missingness due to interval censoring. To handle interval-censored covariates in the Cox proportional hazards model, we propose an available-data estimator, a doubly robust-type estimator as well as the maximum likelihood estimator via EM algorithm and present their asymptotic properties. We also present practical approaches that are valid. We demonstrate the proposed methods using our motivating example from the Northern Manhattan Study. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A Comparison of Methods for Nonparametric Estimation of Item Characteristic Curves for Binary Items

ERIC Educational Resources Information Center

Lee, Young-Sun

2007-01-01

This study compares the performance of three nonparametric item characteristic curve (ICC) estimation procedures: isotonic regression, smoothed isotonic regression, and kernel smoothing. Smoothed isotonic regression, employed along with an appropriate kernel function, provides better estimates and also satisfies the assumption of strict…

A nonparametric analysis of plot basal area growth using tree based models

Treesearch

G. L. Gadbury; H. K. lyer; H. T. Schreuder; C. Y. Ueng

1997-01-01

Tree based statistical models can be used to investigate data structure and predict future observations. We used nonparametric and nonlinear models to reexamine the data sets on tree growth used by Bechtold et al. (1991) and Ruark et al. (1991). The growth data were collected by Forest Inventory and Analysis (FIA) teams from 1962 to 1972 (4th cycle) and 1972 to 1982 (...

Interspecific analysis of covariance structure in the masticatory apparatus of galagos.

PubMed

Vinyard, Christopher J

2007-01-01

The primate masticatory apparatus (MA) is a functionally integrated set of features, each of which performs important functions in biting, ingestive, and chewing behaviors. A comparison of morphological covariance structure among species for these MA features will help us to further understand the evolutionary history of this region. In this exploratory analysis, the covariance structure of the MA is compared across seven galago species to investigate 1) whether there are differences in covariance structure in this region, and 2) if so, how has this covariation changed with respect to size, MA form, diet, and/or phylogeny? Ten measurements of the MA functionally related to bite force production and load resistance were obtained from 218 adults of seven galago species. Correlation matrices were generated for these 10 dimensions and compared among species via matrix correlations and Mantel tests. Subsequently, pairwise covariance disparity in the MA was estimated as a measure of difference in covariance structure between species. Covariance disparity estimates were correlated with pairwise distances related to differences in body size, MA size and shape, genetic distance (based on cytochrome-b sequences) and percentage of dietary foods to determine whether one or more of these factors is linked to differences in covariance structure. Galagos differ in MA covariance structure. Body size appears to be a major factor correlated with differences in covariance structure among galagos. The largest galago species, Otolemur crassicaudatus, exhibits large differences in body mass and covariance structure relative to other galagos, and thus plays a primary role in creating this association. MA size and shape do not correlate with covariance structure when body mass is held constant. Diet also shows no association. Genetic distance is significantly negatively correlated with covariance disparity when body mass is held constant, but this correlation appears to be a function of

Position Error Covariance Matrix Validation and Correction

NASA Technical Reports Server (NTRS)

Frisbee, Joe, Jr.

2016-01-01

In order to calculate operationally accurate collision probabilities, the position error covariance matrices predicted at times of closest approach must be sufficiently accurate representations of the position uncertainties. This presentation will discuss why the Gaussian distribution is a reasonable expectation for the position uncertainty and how this assumed distribution type is used in the validation and correction of position error covariance matrices.

Covariant fields on anti-de Sitter spacetimes

NASA Astrophysics Data System (ADS)

Cotăescu, Ion I.

2018-02-01

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.

Estimating technical efficiency in the hospital sector with panel data: a comparison of parametric and non-parametric techniques.

PubMed

Siciliani, Luigi

2006-01-01

Policy makers are increasingly interested in developing performance indicators that measure hospital efficiency. These indicators may give the purchasers of health services an additional regulatory tool to contain health expenditure. Using panel data, this study compares different parametric (econometric) and non-parametric (linear programming) techniques for the measurement of a hospital's technical efficiency. This comparison was made using a sample of 17 Italian hospitals in the years 1996-9. Highest correlations are found in the efficiency scores between the non-parametric data envelopment analysis under the constant returns to scale assumption (DEA-CRS) and several parametric models. Correlation reduces markedly when using more flexible non-parametric specifications such as data envelopment analysis under the variable returns to scale assumption (DEA-VRS) and the free disposal hull (FDH) model. Correlation also generally reduces when moving from one output to two-output specifications. This analysis suggests that there is scope for developing performance indicators at hospital level using panel data, but it is important that extensive sensitivity analysis is carried out if purchasers wish to make use of these indicators in practice.

Scale-Free Nonparametric Factor Analysis: A User-Friendly Introduction with Concrete Heuristic Examples.

ERIC Educational Resources Information Center

Mittag, Kathleen Cage

Most researchers using factor analysis extract factors from a matrix of Pearson product-moment correlation coefficients. A method is presented for extracting factors in a non-parametric way, by extracting factors from a matrix of Spearman rho (rank correlation) coefficients. It is possible to factor analyze a matrix of association such that…

Tonic and phasic co-variation of peripheral arousal indices in infants

PubMed Central

Wass, S.V.; de Barbaro, K.; Clackson, K.

2015-01-01

Tonic and phasic differences in peripheral autonomic nervous system (ANS) indicators strongly predict differences in attention and emotion regulation in developmental populations. However, virtually all previous research has been based on individual ANS measures, which poses a variety of conceptual and methodlogical challenges to comparing results across studies. Here we recorded heart rate, electrodermal activity (EDA), pupil size, head movement velocity and peripheral accelerometry concurrently while a cohort of 37 typical 12-month-old infants completed a mixed assessment battery lasting approximately 20 min per participant. We analysed covariation of these autonomic indices in three ways: first, tonic (baseline) arousal; second, co-variation in spontaneous (phasic) changes during testing; third, phasic co-variation relative to an external stimulus event. We found that heart rate, head velocity and peripheral accelerometry showed strong positive co-variation across all three analyses. EDA showed no co-variation in tonic activity levels but did show phasic positive co-variation with other measures, that appeared limited to sections of high but not low general arousal. Tonic pupil size showed significant positive covariation, but phasic pupil changes were inconsistent. We conclude that: (i) there is high covariation between autonomic indices in infants, but that EDA may only be sensitive at extreme arousal levels, (ii) that tonic pupil size covaries with other indices, but does not show predicted patterns of phasic change and (iii) that motor activity appears to be a good proxy measure of ANS activity. The strongest patterns of covariation were observed using epoch durations of 40 s per epoch, although significant covariation between indices was also observed using shorter epochs (1 and 5 s). PMID:26316360

Nonparametric spirometry reference values for Hispanic Americans.

PubMed

Glenn, Nancy L; Brown, Vanessa M

2011-02-01

Recent literature sites ethnic origin as a major factor in developing pulmonary function reference values. Extensive studies established reference values for European and African Americans, but not for Hispanic Americans. The Third National Health and Nutrition Examination Survey defines Hispanic as individuals of Spanish speaking cultures. While no group was excluded from the target population, sample size requirements only allowed inclusion of individuals who identified themselves as Mexican Americans. This research constructs nonparametric reference value confidence intervals for Hispanic American pulmonary function. The method is applicable to all ethnicities. We use empirical likelihood confidence intervals to establish normal ranges for reference values. Its major advantage: it is model free, but shares asymptotic properties of model based methods. Statistical comparisons indicate that empirical likelihood interval lengths are comparable to normal theory intervals. Power and efficiency studies agree with previously published theoretical results.

The impact of covariance misspecification in group-based trajectory models for longitudinal data with non-stationary covariance structure.

PubMed

Davies, Christopher E; Glonek, Gary Fv; Giles, Lynne C

2017-08-01

One purpose of a longitudinal study is to gain a better understanding of how an outcome of interest changes among a given population over time. In what follows, a trajectory will be taken to mean the series of measurements of the outcome variable for an individual. Group-based trajectory modelling methods seek to identify subgroups of trajectories within a population, such that trajectories that are grouped together are more similar to each other than to trajectories in distinct groups. Group-based trajectory models generally assume a certain structure in the covariances between measurements, for example conditional independence, homogeneous variance between groups or stationary variance over time. Violations of these assumptions could be expected to result in poor model performance. We used simulation to investigate the effect of covariance misspecification on misclassification of trajectories in commonly used models under a range of scenarios. To do this we defined a measure of performance relative to the ideal Bayesian correct classification rate. We found that the more complex models generally performed better over a range of scenarios. In particular, incorrectly specified covariance matrices could significantly bias the results but using models with a correct but more complicated than necessary covariance matrix incurred little cost.

Perturbative approach to covariance matrix of the matter power spectrum

DOE PAGES

Mohammed, Irshad; Seljak, Uros; Vlah, Zvonimir

2016-12-14

Here, we evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (beat coupling or super-sample variance), and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10\\% level up tomore » $$k \\sim 1 h {\\rm Mpc^{-1}}$$. We also show that all the connected components are dominated by the large-scale modes ($$k<0.1 h {\\rm Mpc^{-1}}$$), regardless of the value of the wavevectors $$k,\\, k'$$ of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher $k$ it is dominated by a single eigenmode. Furthermore, the full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally, we provide a prescription for how to evaluate the covariance matrix from small box simulations without the need to simulate large volumes.« less

Covariance Function for Nearshore Wave Assimilation Systems

DTIC Science & Technology

2018-01-30

covariance can be modeled by a parameterized Gaussian function, for nearshore wave assimilation applications, the covariance function depends primarily on...case of missing values at the compiled time series, the gaps were filled by weighted interpolation. The weights depend on the number of the...averaging, in order to create the continuous time series, filters out the dependency on the instantaneous meteorological and oceanographic conditions

Pu239 Cross-Section Variations Based on Experimental Uncertainties and Covariances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sigeti, David Edward; Williams, Brian J.; Parsons, D. Kent

2016-10-18

Algorithms and software have been developed for producing variations in plutonium-239 neutron cross sections based on experimental uncertainties and covariances. The varied cross-section sets may be produced as random samples from the multi-variate normal distribution defined by an experimental mean vector and covariance matrix, or they may be produced as Latin-Hypercube/Orthogonal-Array samples (based on the same means and covariances) for use in parametrized studies. The variations obey two classes of constraints that are obligatory for cross-section sets and which put related constraints on the mean vector and covariance matrix that detemine the sampling. Because the experimental means and covariances domore » not obey some of these constraints to sufficient precision, imposing the constraints requires modifying the experimental mean vector and covariance matrix. Modification is done with an algorithm based on linear algebra that minimizes changes to the means and covariances while insuring that the operations that impose the different constraints do not conflict with each other.« less

Eliciting Systematic Rule Use in Covariation Judgment [the Early Years].

ERIC Educational Resources Information Center

Shaklee, Harriet; Paszek, Donald

Related research suggests that children may show some simple understanding of event covariations by the early elementary school years. The present experiments use a rule analysis methodology to investigate covariation judgments of children in this age range. In Experiment 1, children in second, third and fourth grade judged covariations on 12…

Robust infrared targets tracking with covariance matrix representation

NASA Astrophysics Data System (ADS)

Cheng, Jian

2009-07-01

Robust infrared target tracking is an important and challenging research topic in many military and security applications, such as infrared imaging guidance, infrared reconnaissance, scene surveillance, etc. To effectively tackle the nonlinear and non-Gaussian state estimation problems, particle filtering is introduced to construct the theory framework of infrared target tracking. Under this framework, the observation probabilistic model is one of main factors for infrared targets tracking performance. In order to improve the tracking performance, covariance matrices are introduced to represent infrared targets with the multi-features. The observation probabilistic model can be constructed by computing the distance between the reference target's and the target samples' covariance matrix. Because the covariance matrix provides a natural tool for integrating multiple features, and is scale and illumination independent, target representation with covariance matrices can hold strong discriminating ability and robustness. Two experimental results demonstrate the proposed method is effective and robust for different infrared target tracking, such as the sensor ego-motion scene, and the sea-clutter scene.

Estimation of spline function in nonparametric path analysis based on penalized weighted least square (PWLS)

NASA Astrophysics Data System (ADS)

Fernandes, Adji Achmad Rinaldo; Solimun, Arisoesilaningsih, Endang

2017-12-01

The aim of this research is to estimate the spline in Path Analysis-based on Nonparametric Regression using Penalized Weighted Least Square (PWLS) approach. Approach used is Reproducing Kernel Hilbert Space at sobolev space. Nonparametric path analysis model on the equation y1 i=f1.1(x1 i)+ε1 i; y2 i=f1.2(x1 i)+f2.2(y1 i)+ε2 i; i =1 ,2 ,…,n Nonparametric Path Analysis which meet the criteria of minimizing PWLS min fw .k∈W2m[aw .k,bw .k], k =1 ,2 { (2n ) -1(y˜-f ˜ ) TΣ-1(y ˜-f ˜ ) + ∑k =1 2 ∑w =1 2 λw .k ∫aw .k bw .k [fw.k (m )(xi) ] 2d xi } is f ˜^=Ay ˜ with A=T1(T1TU1-1∑-1T1)-1T1TU1-1∑-1+V1U1-1∑-1[I-T1(T1TU1-1∑-1T1)-1T1TU1-1∑-1] columnalign="left">+T2(T2TU2-1∑-1T2)-1T2TU2-1∑-1+V2U2-1∑-1[I1-T2(T2TU2-1∑-1T2) -1T2TU2-1∑-1

MEASURING DARK MATTER PROFILES NON-PARAMETRICALLY IN DWARF SPHEROIDALS: AN APPLICATION TO DRACO

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jardel, John R.; Gebhardt, Karl; Fabricius, Maximilian H.

2013-02-15

We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal galaxy (dSph) Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spectrograph on the 2.7 m telescope at McDonald Observatory. Ourmore » non-parametric Schwarzschild models find strong evidence that the dark matter profile in Draco is cuspy for 20 {<=} r {<=} 700 pc. The profile for r {>=} 20 pc is well fit by a power law with slope {alpha} = -1.0 {+-} 0.2, consistent with predictions from cold dark matter simulations. Our models confirm that, despite its low baryon content relative to other dSphs, Draco lives in a massive halo.« less

Application of the LSQR algorithm in non-parametric estimation of aerosol size distribution

NASA Astrophysics Data System (ADS)

He, Zhenzong; Qi, Hong; Lew, Zhongyuan; Ruan, Liming; Tan, Heping; Luo, Kun

2016-05-01

Based on the Least Squares QR decomposition (LSQR) algorithm, the aerosol size distribution (ASD) is retrieved in non-parametric approach. The direct problem is solved by the Anomalous Diffraction Approximation (ADA) and the Lambert-Beer Law. An optimal wavelength selection method is developed to improve the retrieval accuracy of the ASD. The proposed optimal wavelength set is selected by the method which can make the measurement signals sensitive to wavelength and decrease the degree of the ill-condition of coefficient matrix of linear systems effectively to enhance the anti-interference ability of retrieval results. Two common kinds of monomodal and bimodal ASDs, log-normal (L-N) and Gamma distributions, are estimated, respectively. Numerical tests show that the LSQR algorithm can be successfully applied to retrieve the ASD with high stability in the presence of random noise and low susceptibility to the shape of distributions. Finally, the experimental measurement ASD over Harbin in China is recovered reasonably. All the results confirm that the LSQR algorithm combined with the optimal wavelength selection method is an effective and reliable technique in non-parametric estimation of ASD.

Profile local linear estimation of generalized semiparametric regression model for longitudinal data.

PubMed

Sun, Yanqing; Sun, Liuquan; Zhou, Jie

2013-07-01

This paper studies the generalized semiparametric regression model for longitudinal data where the covariate effects are constant for some and time-varying for others. Different link functions can be used to allow more flexible modelling of longitudinal data. The nonparametric components of the model are estimated using a local linear estimating equation and the parametric components are estimated through a profile estimating function. The method automatically adjusts for heterogeneity of sampling times, allowing the sampling strategy to depend on the past sampling history as well as possibly time-dependent covariates without specifically model such dependence. A [Formula: see text]-fold cross-validation bandwidth selection is proposed as a working tool for locating an appropriate bandwidth. A criteria for selecting the link function is proposed to provide better fit of the data. Large sample properties of the proposed estimators are investigated. Large sample pointwise and simultaneous confidence intervals for the regression coefficients are constructed. Formal hypothesis testing procedures are proposed to check for the covariate effects and whether the effects are time-varying. A simulation study is conducted to examine the finite sample performances of the proposed estimation and hypothesis testing procedures. The methods are illustrated with a data example.

Zero- vs. one-dimensional, parametric vs. non-parametric, and confidence interval vs. hypothesis testing procedures in one-dimensional biomechanical trajectory analysis.

PubMed

Pataky, Todd C; Vanrenterghem, Jos; Robinson, Mark A

2015-05-01

Biomechanical processes are often manifested as one-dimensional (1D) trajectories. It has been shown that 1D confidence intervals (CIs) are biased when based on 0D statistical procedures, and the non-parametric 1D bootstrap CI has emerged in the Biomechanics literature as a viable solution. The primary purpose of this paper was to clarify that, for 1D biomechanics datasets, the distinction between 0D and 1D methods is much more important than the distinction between parametric and non-parametric procedures. A secondary purpose was to demonstrate that a parametric equivalent to the 1D bootstrap exists in the form of a random field theory (RFT) correction for multiple comparisons. To emphasize these points we analyzed six datasets consisting of force and kinematic trajectories in one-sample, paired, two-sample and regression designs. Results showed, first, that the 1D bootstrap and other 1D non-parametric CIs were qualitatively identical to RFT CIs, and all were very different from 0D CIs. Second, 1D parametric and 1D non-parametric hypothesis testing results were qualitatively identical for all six datasets. Last, we highlight the limitations of 1D CIs by demonstrating that they are complex, design-dependent, and thus non-generalizable. These results suggest that (i) analyses of 1D data based on 0D models of randomness are generally biased unless one explicitly identifies 0D variables before the experiment, and (ii) parametric and non-parametric 1D hypothesis testing provide an unambiguous framework for analysis when one׳s hypothesis explicitly or implicitly pertains to whole 1D trajectories. Copyright © 2015 Elsevier Ltd. All rights reserved.

Computation of nonparametric convex hazard estimators via profile methods.

PubMed

Jankowski, Hanna K; Wellner, Jon A

2009-05-01

This paper proposes a profile likelihood algorithm to compute the nonparametric maximum likelihood estimator of a convex hazard function. The maximisation is performed in two steps: First the support reduction algorithm is used to maximise the likelihood over all hazard functions with a given point of minimum (or antimode). Then it is shown that the profile (or partially maximised) likelihood is quasi-concave as a function of the antimode, so that a bisection algorithm can be applied to find the maximum of the profile likelihood, and hence also the global maximum. The new algorithm is illustrated using both artificial and real data, including lifetime data for Canadian males and females.

Signs of depth-luminance covariance in 3-D cluttered scenes.

PubMed

Scaccia, Milena; Langer, Michael S

2018-03-01

In three-dimensional (3-D) cluttered scenes such as foliage, deeper surfaces often are more shadowed and hence darker, and so depth and luminance often have negative covariance. We examined whether the sign of depth-luminance covariance plays a role in depth perception in 3-D clutter. We compared scenes rendered with negative and positive depth-luminance covariance where positive covariance means that deeper surfaces are brighter and negative covariance means deeper surfaces are darker. For each scene, the sign of the depth-luminance covariance was given by occlusion cues. We tested whether subjects could use this sign information to judge the depth order of two target surfaces embedded in 3-D clutter. The clutter consisted of distractor surfaces that were randomly distributed in a 3-D volume. We tested three independent variables: the sign of the depth-luminance covariance, the colors of the targets and distractors, and the background luminance. An analysis of variance showed two main effects: Subjects performed better when the deeper surfaces were darker and when the color of the target surfaces was the same as the color of the distractors. There was also a strong interaction: Subjects performed better under a negative depth-luminance covariance condition when targets and distractors had different colors than when they had the same color. Our results are consistent with a "dark means deep" rule, but the use of this rule depends on the similarity between the color of the targets and color of the 3-D clutter.

The Impact of Conditional Scores on the Performance of DETECT.

ERIC Educational Resources Information Center

Zhang, Yanwei Oliver; Yu, Feng; Nandakumar, Ratna

DETECT is a nonparametric, conditional covariance-based procedure to identify dimensional structure and the degree of multidimensionality of test data. The ability composite or conditional score used to estimate conditional covariance plays a significant role in the performance of DETECT. The number correct score of all items in the test (T) and…

Empirical Performance of Covariates in Education Observational Studies

ERIC Educational Resources Information Center

Wong, Vivian C.; Valentine, Jeffrey C.; Miller-Bains, Kate

2017-01-01

This article summarizes results from 12 empirical evaluations of observational methods in education contexts. We look at the performance of three common covariate-types in observational studies where the outcome is a standardized reading or math test. They are: pretest measures, local geographic matching, and rich covariate sets with a strong…

A comparative study between nonlinear regression and nonparametric approaches for modelling Phalaris paradoxa seedling emergence

USDA-ARS?s Scientific Manuscript database

Parametric non-linear regression (PNR) techniques commonly are used to develop weed seedling emergence models. Such techniques, however, require statistical assumptions that are difficult to meet. To examine and overcome these limitations, we compared PNR with a nonparametric estimation technique. F...

An Examination of Parametric and Nonparametric Dimensionality Assessment Methods with Exploratory and Confirmatory Mode

ERIC Educational Resources Information Center

Kogar, Hakan

2018-01-01

The aim of the present research study was to compare the findings from the nonparametric MSA, DIMTEST and DETECT and the parametric dimensionality determining methods in various simulation conditions by utilizing exploratory and confirmatory methods. For this purpose, various simulation conditions were established based on number of dimensions,…

Debt and growth: A non-parametric approach

NASA Astrophysics Data System (ADS)

Brida, Juan Gabriel; Gómez, David Matesanz; Seijas, Maria Nela

2017-11-01

In this study, we explore the dynamic relationship between public debt and economic growth by using a non-parametric approach based on data symbolization and clustering methods. The study uses annual data of general government consolidated gross debt-to-GDP ratio and gross domestic product for sixteen countries between 1977 and 2015. Using symbolic sequences, we introduce a notion of distance between the dynamical paths of different countries. Then, a Minimal Spanning Tree and a Hierarchical Tree are constructed from time series to help detecting the existence of groups of countries sharing similar economic performance. The main finding of the study appears for the period 2008-2016 when several countries surpassed the 90% debt-to-GDP threshold. During this period, three groups (clubs) of countries are obtained: high, mid and low indebted countries, suggesting that the employed debt-to-GDP threshold drives economic dynamics for the selected countries.

Conditional Covariance Theory and Detect for Polytomous Items

ERIC Educational Resources Information Center

Zhang, Jinming

2007-01-01

This paper extends the theory of conditional covariances to polytomous items. It has been proven that under some mild conditions, commonly assumed in the analysis of response data, the conditional covariance of two items, dichotomously or polytomously scored, given an appropriately chosen composite is positive if, and only if, the two items…

New approaches to provide feedback from nuclear and covariance data adjustment for effective improvement of evaluated nuclear data files

NASA Astrophysics Data System (ADS)

Palmiotti, Giuseppe; Salvatores, Massimo; Hursin, Mathieu; Kodeli, Ivo; Gabrielli, Fabrizio; Hummel, Andrew

2017-09-01

A critical examination of the role of uncertainty assessment, target accuracies, role of integral experiment for validation and, consequently, of data adjustments methods is underway since several years at OECD-NEA, the objective being to provide criteria and practical approaches to use effectively the results of sensitivity analyses and cross section adjustments for feedback to evaluators and experimentalists in order to improve without ambiguities the knowledge of neutron cross sections, uncertainties, and correlations to be used in a wide range of applications and to meet new requirements and constraints for innovative reactor and fuel cycle system design. An approach will be described that expands as much as possible the use in the adjustment procedure of selected integral experiments that provide information on "elementary" phenomena, on separated individual physics effects related to specific isotopes or on specific energy ranges. An application to a large experimental data base has been performed and the results are discussed in the perspective of new evaluation projects like the CIELO initiative.

Nonparametric Regression Subject to a Given Number of Local Extreme Value

DTIC Science & Technology

2001-07-01

compilation report: ADP013708 thru ADP013761 UNCLASSIFIED Nonparametric regression subject to a given number of local extreme value Ali Majidi and Laurie...locations of the local extremes for the smoothing algorithm. 280 A. Majidi and L. Davies 3 The smoothing problem We make the smoothing problem precise...is the solution of QP3. k--oo 282 A. Majidi and L. Davies FiG. 2. The captions top-left, top-right, bottom-left, bottom-right show the result of the

Phenotypic covariance at species' borders.

PubMed

Caley, M Julian; Cripps, Edward; Game, Edward T

2013-05-28

Understanding the evolution of species limits is important in ecology, evolution, and conservation biology. Despite its likely importance in the evolution of these limits, little is known about phenotypic covariance in geographically marginal populations, and the degree to which it constrains, or facilitates, responses to selection. We investigated phenotypic covariance in morphological traits at species' borders by comparing phenotypic covariance matrices (P), including the degree of shared structure, the distribution of strengths of pair-wise correlations between traits, the degree of morphological integration of traits, and the ranks of matricies, between central and marginal populations of three species-pairs of coral reef fishes. Greater structural differences in P were observed between populations close to range margins and conspecific populations toward range centres, than between pairs of conspecific populations that were both more centrally located within their ranges. Approximately 80% of all pair-wise trait correlations within populations were greater in the north, but these differences were unrelated to the position of the sampled population with respect to the geographic range of the species. Neither the degree of morphological integration, nor ranks of P, indicated greater evolutionary constraint at range edges. Characteristics of P observed here provide no support for constraint contributing to the formation of these species' borders, but may instead reflect structural change in P caused by selection or drift, and their potential to evolve in the future.

The Performance Analysis Based on SAR Sample Covariance Matrix

PubMed Central

Erten, Esra

2012-01-01

Multi-channel systems appear in several fields of application in science. In the Synthetic Aperture Radar (SAR) context, multi-channel systems may refer to different domains, as multi-polarization, multi-interferometric or multi-temporal data, or even a combination of them. Due to the inherent speckle phenomenon present in SAR images, the statistical description of the data is almost mandatory for its utilization. The complex images acquired over natural media present in general zero-mean circular Gaussian characteristics. In this case, second order statistics as the multi-channel covariance matrix fully describe the data. For practical situations however, the covariance matrix has to be estimated using a limited number of samples, and this sample covariance matrix follow the complex Wishart distribution. In this context, the eigendecomposition of the multi-channel covariance matrix has been shown in different areas of high relevance regarding the physical properties of the imaged scene. Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc. In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community. Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given. PMID:22736976

A consistent covariant quantization of the Brink-Schwarz superparticle

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

We perform the covariant quantization of the ten-dimensional Brink-Schwarz superparticle by reducing it to a system whose constraints are all first class, covariant and have only two levels of reducibility. Research supported by the Rothschild Fellowship.

Estimation for the Linear Model With Uncertain Covariance Matrices

NASA Astrophysics Data System (ADS)

Zachariah, Dave; Shariati, Nafiseh; Bengtsson, Mats; Jansson, Magnus; Chatterjee, Saikat

2014-03-01

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior inverse-Wishart distributions. The nonconvex problem of jointly estimating the signal of interest and the covariance matrices is tackled by a computationally efficient fixed-point iteration as well as an approximate variational Bayes solution. The statistical performance of estimators is compared numerically to state-of-the-art estimators from the literature and shown to perform favorably.

Quantification of Covariance in Tropical Cyclone Activity across Teleconnected Basins

NASA Astrophysics Data System (ADS)

Tolwinski-Ward, S. E.; Wang, D.

2015-12-01

Rigorous statistical quantification of natural hazard covariance across regions has important implications for risk management, and is also of fundamental scientific interest. We present a multivariate Bayesian Poisson regression model for inferring the covariance in tropical cyclone (TC) counts across multiple ocean basins and across Saffir-Simpson intensity categories. Such covariability results from the influence of large-scale modes of climate variability on local environments that can alternately suppress or enhance TC genesis and intensification, and our model also simultaneously quantifies the covariance of TC counts with various climatic modes in order to deduce the source of inter-basin TC covariability. The model explicitly treats the time-dependent uncertainty in observed maximum sustained wind data, and hence the nominal intensity category of each TC. Differences in annual TC counts as measured by different agencies are also formally addressed. The probabilistic output of the model can be probed for probabilistic answers to such questions as: - Does the relationship between different categories of TCs differ statistically by basin? - Which climatic predictors have significant relationships with TC activity in each basin? - Are the relationships between counts in different basins conditionally independent given the climatic predictors, or are there other factors at play affecting inter-basin covariability? - How can a portfolio of insured property be optimized across space to minimize risk? Although we present results of our model applied to TCs, the framework is generalizable to covariance estimation between multivariate counts of natural hazards across regions and/or across peril types.

Robust non-parametric one-sample tests for the analysis of recurrent events.

PubMed

Rebora, Paola; Galimberti, Stefania; Valsecchi, Maria Grazia

2010-12-30

One-sample non-parametric tests are proposed here for inference on recurring events. The focus is on the marginal mean function of events and the basis for inference is the standardized distance between the observed and the expected number of events under a specified reference rate. Different weights are considered in order to account for various types of alternative hypotheses on the mean function of the recurrent events process. A robust version and a stratified version of the test are also proposed. The performance of these tests was investigated through simulation studies under various underlying event generation processes, such as homogeneous and nonhomogeneous Poisson processes, autoregressive and renewal processes, with and without frailty effects. The robust versions of the test have been shown to be suitable in a wide variety of event generating processes. The motivating context is a study on gene therapy in a very rare immunodeficiency in children, where a major end-point is the recurrence of severe infections. Robust non-parametric one-sample tests for recurrent events can be useful to assess efficacy and especially safety in non-randomized studies or in epidemiological studies for comparison with a standard population. Copyright © 2010 John Wiley & Sons, Ltd.

Covariance and correlation estimation in electron-density maps.

PubMed

Altomare, Angela; Cuocci, Corrado; Giacovazzo, Carmelo; Moliterni, Anna; Rizzi, Rosanna

2012-03-01

Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218; Giacovazzo et al. (2011). Acta Cryst. A67, 368-382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final stages of the structure refinement; a general formula is obtained taking into account both phase and measurement uncertainty, valid at any stage of the crystal structure solution.

Empirically Estimable Classification Bounds Based on a Nonparametric Divergence Measure

PubMed Central

Berisha, Visar; Wisler, Alan; Hero, Alfred O.; Spanias, Andreas

2015-01-01

Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the same distribution and for the case where there exists some mismatch between training and test distributions. We confirm the theoretical results by designing feature selection algorithms using the criteria from these bounds and by evaluating the algorithms on a series of pathological speech classification tasks. PMID:26807014

Asymptotics of nonparametric L-1 regression models with dependent data

PubMed Central

ZHAO, ZHIBIAO; WEI, YING; LIN, DENNIS K.J.

2013-01-01

We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration. PMID:24955016

Investigation of a Nonparametric Procedure for Assessing Goodness-of-Fit in Item Response Theory

ERIC Educational Resources Information Center

Wells, Craig S.; Bolt, Daniel M.

2008-01-01

Tests of model misfit are often performed to validate the use of a particular model in item response theory. Douglas and Cohen (2001) introduced a general nonparametric approach for detecting misfit under the two-parameter logistic model. However, the statistical properties of their approach, and empirical comparisons to other methods, have not…

Measurement Error in Nonparametric Item Response Curve Estimation. Research Report. ETS RR-11-28

ERIC Educational Resources Information Center

Guo, Hongwen; Sinharay, Sandip

2011-01-01

Nonparametric, or kernel, estimation of item response curve (IRC) is a concern theoretically and operationally. Accuracy of this estimation, often used in item analysis in testing programs, is biased when the observed scores are used as the regressor because the observed scores are contaminated by measurement error. In this study, we investigate…

Effect of correlation on covariate selection in linear and nonlinear mixed effect models.

PubMed

Bonate, Peter L

2017-01-01

The effect of correlation among covariates on covariate selection was examined with linear and nonlinear mixed effect models. Demographic covariates were extracted from the National Health and Nutrition Examination Survey III database. Concentration-time profiles were Monte Carlo simulated where only one covariate affected apparent oral clearance (CL/F). A series of univariate covariate population pharmacokinetic models was fit to the data and compared with the reduced model without covariate. The "best" covariate was identified using either the likelihood ratio test statistic or AIC. Weight and body surface area (calculated using Gehan and George equation, 1970) were highly correlated (r = 0.98). Body surface area was often selected as a better covariate than weight, sometimes as high as 1 in 5 times, when weight was the covariate used in the data generating mechanism. In a second simulation, parent drug concentration and three metabolites were simulated from a thorough QT study and used as covariates in a series of univariate linear mixed effects models of ddQTc interval prolongation. The covariate with the largest significant LRT statistic was deemed the "best" predictor. When the metabolite was formation-rate limited and only parent concentrations affected ddQTc intervals the metabolite was chosen as a better predictor as often as 1 in 5 times depending on the slope of the relationship between parent concentrations and ddQTc intervals. A correlated covariate can be chosen as being a better predictor than another covariate in a linear or nonlinear population analysis by sheer correlation These results explain why for the same drug different covariates may be identified in different analyses. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Non-parametric diffeomorphic image registration with the demons algorithm.

PubMed

Vercauteren, Tom; Pennec, Xavier; Perchant, Aymeric; Ayache, Nicholas

2007-01-01

We propose a non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. The demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. The main idea of our algorithm is to adapt this procedure to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of free form deformations by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the true ones in terms of Jacobians.

Stable Estimation of a Covariance Matrix Guided by Nuclear Norm Penalties

PubMed Central

Chi, Eric C.; Lange, Kenneth

2014-01-01

Estimation of a covariance matrix or its inverse plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. The current paper introduces a novel prior to ensure a well-conditioned maximum a posteriori (MAP) covariance estimate. The prior shrinks the sample covariance estimator towards a stable target and leads to a MAP estimator that is consistent and asymptotically efficient. Thus, the MAP estimator gracefully transitions towards the sample covariance matrix as the number of samples grows relative to the number of covariates. The utility of the MAP estimator is demonstrated in two standard applications – discriminant analysis and EM clustering – in this sampling regime. PMID:25143662

New approaches to provide feedback from nuclear and covariance data adjustment for effective improvement of evaluated nuclear data files

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palmiotti, Giuseppe; Salvatores, Massimo; Hursin, Mathieu

2016-11-01

A critical examination of the role of uncertainty assessment, target accuracies, role of integral experiment for validation and, consequently, of data adjustments methods is underway since several years at OECD-NEA, the objective being to provide criteria and practical approaches to use effectively the results of sensitivity analyses and cross section adjustments for feedback to evaluators and experimentalists in order to improve without ambiguities the knowledge of neutron cross sections, uncertainties, and correlations to be used in a wide range of applications and to meet new requirements and constraints for innovative reactor and fuel cycle system design. An approach will bemore » described that expands as much as possible the use in the adjustment procedure of selected integral experiments that provide information on “elementary” phenomena, on separated individual physics effects related to specific isotopes or on specific energy ranges. An application to a large experimental data base has been performed and the results are discussed in the perspective of new evaluation projects like the CIELO initiative.« less

Nonparametric bootstrap analysis with applications to demographic effects in demand functions.

PubMed

Gozalo, P L

1997-12-01

"A new bootstrap proposal, labeled smooth conditional moment (SCM) bootstrap, is introduced for independent but not necessarily identically distributed data, where the classical bootstrap procedure fails.... A good example of the benefits of using nonparametric and bootstrap methods is the area of empirical demand analysis. In particular, we will be concerned with their application to the study of two important topics: what are the most relevant effects of household demographic variables on demand behavior, and to what extent present parametric specifications capture these effects." excerpt

Parametric number covariance in quantum chaotic spectra.

PubMed

Vinayak; Kumar, Sandeep; Pandey, Akhilesh

2016-03-01

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.

Cortisol Covariation Within Parents of Young Children: Moderation by Relationship Aggression

PubMed Central

Saxbe, Darby E.; Adam, Emma K.; Dunkel Schetter, Christine; Guardino, Christine M.; Simon, Clarissa; McKinney, Chelsea O.; Shalowitz, Madeleine U.; Shriver, Eunice Kennedy

2015-01-01

Covariation in diurnal cortisol has been observed in several studies of cohabiting couples. In two such studies (Liu et al, 2013, Saxbe & Repetti, 2010), relationship distress was associated with stronger within-couple correlations, suggesting that couples’ physiological linkage with each other may indicate problematic dyadic functioning. Although intimate partner aggression has been associated with dysregulation in women’s diurnal cortisol, it has not yet been tested as a moderator of within-couple covariation. This study reports on a diverse sample of 122 parents who sampled salivary cortisol on matched days for two years following the birth of an infant. Partners showed strong positive cortisol covariation. In couples with higher levels of partner-perpetrated aggression reported by women at one year postpartum, both women and men had a flatter diurnal decrease in cortisol and stronger correlations with partners’ cortisol sampled at the same timepoints. In other words, relationship aggression was linked both with indices of suboptimal cortisol rhythms in both members of the couples and with stronger within-couple covariation coefficients. These results persisted when relationship satisfaction and demographic covariates were included in the model. During some of the sampling days, some women were pregnant with a subsequent child, but pregnancy did not significantly moderate cortisol levels or within-couple covariation. The findings suggest that couples experiencing relationship aggression have both suboptimal neuroendocrine profiles and stronger covariation. Cortisol covariation is an understudied phenomenon with potential implications for couples’ relationship functioning and physical health. PMID:26298691

Parametric and Nonparametric Statistical Methods for Genomic Selection of Traits with Additive and Epistatic Genetic Architectures

PubMed Central

Howard, Réka; Carriquiry, Alicia L.; Beavis, William D.

2014-01-01

Parametric and nonparametric methods have been developed for purposes of predicting phenotypes. These methods are based on retrospective analyses of empirical data consisting of genotypic and phenotypic scores. Recent reports have indicated that parametric methods are unable to predict phenotypes of traits with known epistatic genetic architectures. Herein, we review parametric methods including least squares regression, ridge regression, Bayesian ridge regression, least absolute shrinkage and selection operator (LASSO), Bayesian LASSO, best linear unbiased prediction (BLUP), Bayes A, Bayes B, Bayes C, and Bayes Cπ. We also review nonparametric methods including Nadaraya-Watson estimator, reproducing kernel Hilbert space, support vector machine regression, and neural networks. We assess the relative merits of these 14 methods in terms of accuracy and mean squared error (MSE) using simulated genetic architectures consisting of completely additive or two-way epistatic interactions in an F2 population derived from crosses of inbred lines. Each simulated genetic architecture explained either 30% or 70% of the phenotypic variability. The greatest impact on estimates of accuracy and MSE was due to genetic architecture. Parametric methods were unable to predict phenotypic values when the underlying genetic architecture was based entirely on epistasis. Parametric methods were slightly better than nonparametric methods for additive genetic architectures. Distinctions among parametric methods for additive genetic architectures were incremental. Heritability, i.e., proportion of phenotypic variability, had the second greatest impact on estimates of accuracy and MSE. PMID:24727289

Marginalized zero-inflated Poisson models with missing covariates.

PubMed

Benecha, Habtamu K; Preisser, John S; Divaris, Kimon; Herring, Amy H; Das, Kalyan

2018-05-11

Unlike zero-inflated Poisson regression, marginalized zero-inflated Poisson (MZIP) models for counts with excess zeros provide estimates with direct interpretations for the overall effects of covariates on the marginal mean. In the presence of missing covariates, MZIP and many other count data models are ordinarily fitted using complete case analysis methods due to lack of appropriate statistical methods and software. This article presents an estimation method for MZIP models with missing covariates. The method, which is applicable to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data on the caries preventive effects of a school-based fluoride mouthrinse program. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

An Empirical State Error Covariance Matrix Orbit Determination Example

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2015-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance

School-related adjustment in children and adolescents with CHD.

PubMed

Im, Yu-Mi; Lee, Sunhee; Yun, Tae-Jin; Choi, Jae Young

2017-09-01

Advancements in medical and surgical treatment have increased the life expectancy of patients with CHD. Many patients with CHD, however, struggle with the medical, psychosocial, and behavioural challenges as they transition from childhood to adulthood. Specifically, the environmental and lifestyle challenges in school are very important factors that affect children and adolescents with CHD. This study aimed to evaluate school-related adjustments depending on school level and disclosure of disease in children and adolescents with CHD. This was a descriptive and exploratory study with 205 children and adolescents, aged 7-18 years, who were recruited from two congenital heart clinics from 5 January to 27 February, 2015. Data were analysed using the Student's t-test, analysis of variance, and a univariate general linear model. School-related adjustment scores were significantly different according to school level and disclosure of disease (p<0.001) when age, religion, experience being bullied, and parents' educational levels were assigned as covariates. The school-related adjustment score of patients who did not disclose their disease dropped significantly in high school. This indicated that it is important for healthcare providers to plan developmentally appropriate educational transition programmes for middle-school students with CHD in order for students to prepare themselves before entering high school.

Comparison of Parametric and Nonparametric Bootstrap Methods for Estimating Random Error in Equipercentile Equating

ERIC Educational Resources Information Center

Cui, Zhongmin; Kolen, Michael J.

2008-01-01

This article considers two methods of estimating standard errors of equipercentile equating: the parametric bootstrap method and the nonparametric bootstrap method. Using a simulation study, these two methods are compared under three sample sizes (300, 1,000, and 3,000), for two test content areas (the Iowa Tests of Basic Skills Maps and Diagrams…

An Assessment of the Nonparametric Approach for Evaluating the Fit of Item Response Models

ERIC Educational Resources Information Center

Liang, Tie; Wells, Craig S.; Hambleton, Ronald K.

2014-01-01

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

Galaxy two-point covariance matrix estimation for next generation surveys

NASA Astrophysics Data System (ADS)

Howlett, Cullan; Percival, Will J.

2017-12-01

We perform a detailed analysis of the covariance matrix of the spherically averaged galaxy power spectrum and present a new, practical method for estimating this within an arbitrary survey without the need for running mock galaxy simulations that cover the full survey volume. The method uses theoretical arguments to modify the covariance matrix measured from a set of small-volume cubic galaxy simulations, which are computationally cheap to produce compared to larger simulations and match the measured small-scale galaxy clustering more accurately than is possible using theoretical modelling. We include prescriptions to analytically account for the window function of the survey, which convolves the measured covariance matrix in a non-trivial way. We also present a new method to include the effects of super-sample covariance and modes outside the small simulation volume which requires no additional simulations and still allows us to scale the covariance matrix. As validation, we compare the covariance matrix estimated using our new method to that from a brute-force calculation using 500 simulations originally created for analysis of the Sloan Digital Sky Survey Main Galaxy Sample. We find excellent agreement on all scales of interest for large-scale structure analysis, including those dominated by the effects of the survey window, and on scales where theoretical models of the clustering normally break down, but the new method produces a covariance matrix with significantly better signal-to-noise ratio. Although only formally correct in real space, we also discuss how our method can be extended to incorporate the effects of redshift space distortions.

Altered Cerebral Blood Flow Covariance Network in Schizophrenia.

PubMed

Liu, Feng; Zhuo, Chuanjun; Yu, Chunshui

2016-01-01

Many studies have shown abnormal cerebral blood flow (CBF) in schizophrenia; however, it remains unclear how topological properties of CBF network are altered in this disorder. Here, arterial spin labeling (ASL) MRI was employed to measure resting-state CBF in 96 schizophrenia patients and 91 healthy controls. CBF covariance network of each group was constructed by calculating across-subject CBF covariance between 90 brain regions. Graph theory was used to compare intergroup differences in global and nodal topological measures of the network. Both schizophrenia patients and healthy controls had small-world topology in CBF covariance networks, implying an optimal balance between functional segregation and integration. Compared with healthy controls, schizophrenia patients showed reduced small-worldness, normalized clustering coefficient and local efficiency of the network, suggesting a shift toward randomized network topology in schizophrenia. Furthermore, schizophrenia patients exhibited altered nodal centrality in the perceptual-, affective-, language-, and spatial-related regions, indicating functional disturbance of these systems in schizophrenia. This study demonstrated for the first time that schizophrenia patients have disrupted topological properties in CBF covariance network, which provides a new perspective (efficiency of blood flow distribution between brain regions) for understanding neural mechanisms of schizophrenia.

Phenotypic covariance at species’ borders

PubMed Central

2013-01-01

Background Understanding the evolution of species limits is important in ecology, evolution, and conservation biology. Despite its likely importance in the evolution of these limits, little is known about phenotypic covariance in geographically marginal populations, and the degree to which it constrains, or facilitates, responses to selection. We investigated phenotypic covariance in morphological traits at species’ borders by comparing phenotypic covariance matrices (P), including the degree of shared structure, the distribution of strengths of pair-wise correlations between traits, the degree of morphological integration of traits, and the ranks of matricies, between central and marginal populations of three species-pairs of coral reef fishes. Results Greater structural differences in P were observed between populations close to range margins and conspecific populations toward range centres, than between pairs of conspecific populations that were both more centrally located within their ranges. Approximately 80% of all pair-wise trait correlations within populations were greater in the north, but these differences were unrelated to the position of the sampled population with respect to the geographic range of the species. Conclusions Neither the degree of morphological integration, nor ranks of P, indicated greater evolutionary constraint at range edges. Characteristics of P observed here provide no support for constraint contributing to the formation of these species’ borders, but may instead reflect structural change in P caused by selection or drift, and their potential to evolve in the future. PMID:23714580

Current risks of HeartMate II pump thrombosis: Non-parametric analysis of Interagency Registry for Mechanically Assisted Circulatory Support data.

PubMed

Smedira, Nicholas G; Blackstone, Eugene H; Ehrlinger, John; Thuita, Lucy; Pierce, Christopher D; Moazami, Nader; Starling, Randall C

2015-12-01

Data from 3 institutions revealed an abrupt increase in HeartMate II (Thoratec) pump thrombosis starting in 2011, associated with 48% mortality at 6 months without transplantation or pump exchange. We sought to discover if the increase occurred nationwide in Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS) data, and if so (1) determine if accelerated risk continued, (2) identify predictors, (3) investigate institutional variability, and (4) assess mortality after pump thrombosis. From April 2008 to June 2014, 11,123 HeartMate II devices were implanted at 146 institutions. Machine learning, non-parametric Random Forests for Survival was used to explore risk-adjusted thrombosis based on 87 pre-implant and implant variables, including implant date. A total of 995 pumps thrombosed, with risk peaking within weeks of implant. The risk-adjusted increase in pump thrombosis began in 2010, reached a maximum in 2012, and then plateaued at a level that was 3.3-times higher than pre-2010. Pump exchange, younger age, and larger body mass index were important predictors, and institutional variability was largely explained by implant date, patient profile, and duration of support. The probability of death within 3 months after pump thrombosis was 24%. Accelerated risk of HeartMate II thrombosis was confirmed by Interagency Registry for Mechanically Assisted Circulatory Support data, with risk subsequently leveling at a risk-adjusted rate higher than observed pre-2010. This elevated thrombosis risk emphasizes the need for improved mechanical circulatory support systems and post-market surveillance of adverse events. Clinicians cognizant of these new data should incorporate them into their and their patients' expectations and understanding of risks relative to those of transplantation and continued medical therapy. Copyright © 2015 International Society for Heart and Lung Transplantation. Published by Elsevier Inc. All rights reserved.

Parametric and nonparametric Granger causality testing: Linkages between international stock markets

NASA Astrophysics Data System (ADS)

De Gooijer, Jan G.; Sivarajasingham, Selliah

2008-04-01

This study investigates long-term linear and nonlinear causal linkages among eleven stock markets, six industrialized markets and five emerging markets of South-East Asia. We cover the period 1987-2006, taking into account the on-set of the Asian financial crisis of 1997. We first apply a test for the presence of general nonlinearity in vector time series. Substantial differences exist between the pre- and post-crisis period in terms of the total number of significant nonlinear relationships. We then examine both periods, using a new nonparametric test for Granger noncausality and the conventional parametric Granger noncausality test. One major finding is that the Asian stock markets have become more internationally integrated after the Asian financial crisis. An exception is the Sri Lankan market with almost no significant long-term linear and nonlinear causal linkages with other markets. To ensure that any causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VAR filtered residuals and VAR filtered squared residuals for the post-crisis sample. We find quite a few remaining significant bi- and uni-directional causal nonlinear relationships in these series. Finally, after filtering the VAR-residuals with GARCH-BEKK models, we show that the nonparametric test statistics are substantially smaller in both magnitude and statistical significance than those before filtering. This indicates that nonlinear causality can, to a large extent, be explained by simple volatility effects.

Covariant n/sup 2/-plet mass formulas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidson, A.

Using a generalized internal symmetry group analogous to the Lorentz group, we have constructed a covariant n/sup 2/-plet mass operator. This operator is built as a scalar matrix in the (n;n*) representation, and its SU(n) breaking parameters are identified as intrinsic boost ones. Its basic properties are: covariance, Hermiticity, positivity, charge conjugation, quark contents, and a self-consistent n/sup 2/-1, 1 mixing. The GMO and the Okubo formulas are obtained by considering two different limits of the same generalized mass formula.

Covariance Based Pre-Filters and Screening Criteria for Conjunction Analysis

NASA Astrophysics Data System (ADS)

George, E., Chan, K.

2012-09-01

Several relationships are developed relating object size, initial covariance and range at closest approach to probability of collision. These relationships address the following questions: - Given the objects' initial covariance and combined hard body size, what is the maximum possible value of the probability of collision (Pc)? - Given the objects' initial covariance, what is the maximum combined hard body radius for which the probability of collision does not exceed the tolerance limit? - Given the objects' initial covariance and the combined hard body radius, what is the minimum miss distance for which the probability of collision does not exceed the tolerance limit? - Given the objects' initial covariance and the miss distance, what is the maximum combined hard body radius for which the probability of collision does not exceed the tolerance limit? The first relationship above allows the elimination of object pairs from conjunction analysis (CA) on the basis of the initial covariance and hard-body sizes of the objects. The application of this pre-filter to present day catalogs with estimated covariance results in the elimination of approximately 35% of object pairs as unable to ever conjunct with a probability of collision exceeding 1x10-6. Because Pc is directly proportional to object size and inversely proportional to covariance size, this pre-filter will have a significantly larger impact on future catalogs, which are expected to contain a much larger fraction of small debris tracked only by a limited subset of available sensors. This relationship also provides a mathematically rigorous basis for eliminating objects from analysis entirely based on element set age or quality - a practice commonly done by rough rules of thumb today. Further, these relations can be used to determine the required geometric screening radius for all objects. This analysis reveals the screening volumes for small objects are much larger than needed, while the screening volumes for

Dynamic Tasking of Networked Sensors Using Covariance Information

DTIC Science & Technology

2010-09-01

has been created under an effort called TASMAN (Tasking Autonomous Sensors in a Multiple Application Network). One of the first studies utilizing this...environment was focused on a novel resource management approach, namely covariance-based tasking. Under this scheme, the state error covariance of...resident space objects (RSO), sensor characteristics, and sensor- target geometry were used to determine the effectiveness of future observations in

VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS

PubMed Central

Huang, Jian; Horowitz, Joel L.; Wei, Fengrong

2010-01-01

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is “small” relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component selection becomes that of selecting the groups of coefficients in the expansion. We apply the adaptive group Lasso to select nonzero components, using the group Lasso to obtain an initial estimator and reduce the dimension of the problem. We give conditions under which the group Lasso selects a model whose number of components is comparable with the underlying model, and the adaptive group Lasso selects the nonzero components correctly with probability approaching one as the sample size increases and achieves the optimal rate of convergence. The results of Monte Carlo experiments show that the adaptive group Lasso procedure works well with samples of moderate size. A data example is used to illustrate the application of the proposed method. PMID:21127739

Cortisol covariation within parents of young children: Moderation by relationship aggression.

PubMed

Saxbe, Darby E; Adam, Emma K; Schetter, Christine Dunkel; Guardino, Christine M; Simon, Clarissa; McKinney, Chelsea O; Shalowitz, Madeleine U

2015-12-01

Covariation in diurnal cortisol has been observed in several studies of cohabiting couples. In two such studies (Liu et al., 2013; Saxbe and Repetti, 2010), relationship distress was associated with stronger within-couple correlations, suggesting that couples' physiological linkage with each other may indicate problematic dyadic functioning. Although intimate partner aggression has been associated with dysregulation in women's diurnal cortisol, it has not yet been tested as a moderator of within-couple covariation. This study reports on a diverse sample of 122 parents who sampled salivary cortisol on matched days for two years following the birth of an infant. Partners showed strong positive cortisol covariation. In couples with higher levels of partner-perpetrated aggression reported by women at one year postpartum, both women and men had a flatter diurnal decrease in cortisol and stronger correlations with partners' cortisol sampled at the same timepoints. In other words, relationship aggression was linked both with indices of suboptimal cortisol rhythms in both members of the couples and with stronger within-couple covariation coefficients. These results persisted when relationship satisfaction and demographic covariates were included in the model. During some of the sampling days, some women were pregnant with a subsequent child, but pregnancy did not significantly moderate cortisol levels or within-couple covariation. The findings suggest that couples experiencing relationship aggression have both suboptimal neuroendocrine profiles and stronger covariation. Cortisol covariation is an understudied phenomenon with potential implications for couples' relationship functioning and physical health. Copyright © 2015 Elsevier Ltd. All rights reserved.

Measuring firm size distribution with semi-nonparametric densities

NASA Astrophysics Data System (ADS)

Cortés, Lina M.; Mora-Valencia, Andrés; Perote, Javier

2017-11-01

In this article, we propose a new methodology based on a (log) semi-nonparametric (log-SNP) distribution that nests the lognormal and enables better fits in the upper tail of the distribution through the introduction of new parameters. We test the performance of the lognormal and log-SNP distributions capturing firm size, measured through a sample of US firms in 2004-2015. Taking different levels of aggregation by type of economic activity, our study shows that the log-SNP provides a better fit of the firm size distribution. We also formally introduce the multivariate log-SNP distribution, which encompasses the multivariate lognormal, to analyze the estimation of the joint distribution of the value of the firm's assets and sales. The results suggest that sales are a better firm size measure, as indicated by other studies in the literature.

Bayesian semiparametric estimation of covariate-dependent ROC curves

PubMed Central

Rodríguez, Abel; Martínez, Julissa C.

2014-01-01

Receiver operating characteristic (ROC) curves are widely used to measure the discriminating power of medical tests and other classification procedures. In many practical applications, the performance of these procedures can depend on covariates such as age, naturally leading to a collection of curves associated with different covariate levels. This paper develops a Bayesian heteroscedastic semiparametric regression model and applies it to the estimation of covariate-dependent ROC curves. More specifically, our approach uses Gaussian process priors to model the conditional mean and conditional variance of the biomarker of interest for each of the populations under study. The model is illustrated through an application to the evaluation of prostate-specific antigen for the diagnosis of prostate cancer, which contrasts the performance of our model against alternative models. PMID:24174579

Hawking radiation and covariant anomalies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Rabin; Kulkarni, Shailesh

2008-01-15

Generalizing the method of Wilczek and collaborators we provide a derivation of Hawking radiation from charged black holes using only covariant gauge and gravitational anomalies. The reliability and universality of the anomaly cancellation approach to Hawking radiation is also discussed.

An Empirical State Error Covariance Matrix for Batch State Estimation

NASA Technical Reports Server (NTRS)

Frisbee, Joseph H., Jr.

2011-01-01

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the

Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators: Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators

DOE PAGES

Staid, Andrea; Watson, Jean -Paul; Wets, Roger J. -B.; ...

2017-07-11

Forecasts of available wind power are critical in key electric power systems operations planning problems, including economic dispatch and unit commitment. Such forecasts are necessarily uncertain, limiting the reliability and cost effectiveness of operations planning models based on a single deterministic or “point” forecast. A common approach to address this limitation involves the use of a number of probabilistic scenarios, each specifying a possible trajectory of wind power production, with associated probability. We present and analyze a novel method for generating probabilistic wind power scenarios, leveraging available historical information in the form of forecasted and corresponding observed wind power timemore » series. We estimate non-parametric forecast error densities, specifically using epi-spline basis functions, allowing us to capture the skewed and non-parametric nature of error densities observed in real-world data. We then describe a method to generate probabilistic scenarios from these basis functions that allows users to control for the degree to which extreme errors are captured.We compare the performance of our approach to the current state-of-the-art considering publicly available data associated with the Bonneville Power Administration, analyzing aggregate production of a number of wind farms over a large geographic region. Finally, we discuss the advantages of our approach in the context of specific power systems operations planning problems: stochastic unit commitment and economic dispatch. Here, our methodology is embodied in the joint Sandia – University of California Davis Prescient software package for assessing and analyzing stochastic operations strategies.« less

Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators: Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Staid, Andrea; Watson, Jean -Paul; Wets, Roger J. -B.

Forecasts of available wind power are critical in key electric power systems operations planning problems, including economic dispatch and unit commitment. Such forecasts are necessarily uncertain, limiting the reliability and cost effectiveness of operations planning models based on a single deterministic or “point” forecast. A common approach to address this limitation involves the use of a number of probabilistic scenarios, each specifying a possible trajectory of wind power production, with associated probability. We present and analyze a novel method for generating probabilistic wind power scenarios, leveraging available historical information in the form of forecasted and corresponding observed wind power timemore » series. We estimate non-parametric forecast error densities, specifically using epi-spline basis functions, allowing us to capture the skewed and non-parametric nature of error densities observed in real-world data. We then describe a method to generate probabilistic scenarios from these basis functions that allows users to control for the degree to which extreme errors are captured.We compare the performance of our approach to the current state-of-the-art considering publicly available data associated with the Bonneville Power Administration, analyzing aggregate production of a number of wind farms over a large geographic region. Finally, we discuss the advantages of our approach in the context of specific power systems operations planning problems: stochastic unit commitment and economic dispatch. Here, our methodology is embodied in the joint Sandia – University of California Davis Prescient software package for assessing and analyzing stochastic operations strategies.« less

A Flexible Spatio-Temporal Model for Air Pollution with Spatial and Spatio-Temporal Covariates.

PubMed

Lindström, Johan; Szpiro, Adam A; Sampson, Paul D; Oron, Assaf P; Richards, Mark; Larson, Tim V; Sheppard, Lianne

2014-09-01

The development of models that provide accurate spatio-temporal predictions of ambient air pollution at small spatial scales is of great importance for the assessment of potential health effects of air pollution. Here we present a spatio-temporal framework that predicts ambient air pollution by combining data from several different monitoring networks and deterministic air pollution model(s) with geographic information system (GIS) covariates. The model presented in this paper has been implemented in an R package, SpatioTemporal, available on CRAN. The model is used by the EPA funded Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air) to produce estimates of ambient air pollution; MESA Air uses the estimates to investigate the relationship between chronic exposure to air pollution and cardiovascular disease. In this paper we use the model to predict long-term average concentrations of NO x in the Los Angeles area during a ten year period. Predictions are based on measurements from the EPA Air Quality System, MESA Air specific monitoring, and output from a source dispersion model for traffic related air pollution (Caline3QHCR). Accuracy in predicting long-term average concentrations is evaluated using an elaborate cross-validation setup that accounts for a sparse spatio-temporal sampling pattern in the data, and adjusts for temporal effects. The predictive ability of the model is good with cross-validated R 2 of approximately 0.7 at subject sites. Replacing four geographic covariate indicators of traffic density with the Caline3QHCR dispersion model output resulted in very similar prediction accuracy from a more parsimonious and more interpretable model. Adding traffic-related geographic covariates to the model that included Caline3QHCR did not further improve the prediction accuracy.

Covariant balance laws in continua with microstructure

NASA Astrophysics Data System (ADS)

Yavari, Arash; Marsden, Jerrold E.

2009-02-01

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas. We model a structured continuum as a triplet of Riemannian manifolds: a material manifold, the ambient space manifold of material particles and a director field manifold. The Green-Naghdi-Rivlin theorem and its extensions for structured continua are critically reviewed. We show that when the ambient space is Euclidean and when the microstructure manifold is the tangent space of the ambient space manifold, postulating a single balance of energy law and its invariance under time-dependent isometries of the ambient space, one obtains conservation of mass, balances of linear and angular momenta but not a separate balance of linear momentum. We develop a covariant elasticity theory for structured continua by postulating that energy balance is invariant under time-dependent spatial diffeomorphisms of the ambient space, which in this case is the product of two Riemannian manifolds. We then introduce two types of constrained continua in which microstructure manifold is linked to the reference and ambient space manifolds. In the case when at every material point, the microstructure manifold is the tangent space of the ambient space manifold at the image of the material point, we show that the assumption of covariance leads to balances of linear and angular momenta with contributions from both forces and micro-forces along with two Doyle-Ericksen formulas. We show that generalized covariance leads to two balances of linear momentum and a single coupled balance of angular momentum. Using this theory, we covariantly obtain the balance laws for two specific examples, namely elastic

Structural and Maturational Covariance in Early Childhood Brain Development.

PubMed

Geng, Xiujuan; Li, Gang; Lu, Zhaohua; Gao, Wei; Wang, Li; Shen, Dinggang; Zhu, Hongtu; Gilmore, John H

2017-03-01

Brain structural covariance networks (SCNs) composed of regions with correlated variation are altered in neuropsychiatric disease and change with age. Little is known about the development of SCNs in early childhood, a period of rapid cortical growth. We investigated the development of structural and maturational covariance networks, including default, dorsal attention, primary visual and sensorimotor networks in a longitudinal population of 118 children after birth to 2 years old and compared them with intrinsic functional connectivity networks. We found that structural covariance of all networks exhibit strong correlations mostly limited to their seed regions. By Age 2, default and dorsal attention structural networks are much less distributed compared with their functional maps. The maturational covariance maps, however, revealed significant couplings in rates of change between distributed regions, which partially recapitulate their functional networks. The structural and maturational covariance of the primary visual and sensorimotor networks shows similar patterns to the corresponding functional networks. Results indicate that functional networks are in place prior to structural networks, that correlated structural patterns in adult may arise in part from coordinated cortical maturation, and that regional co-activation in functional networks may guide and refine the maturation of SCNs over childhood development. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

ARMA Cholesky Factor Models for the Covariance Matrix of Linear Models.

PubMed

Lee, Keunbaik; Baek, Changryong; Daniels, Michael J

2017-11-01

In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.

Covariant conserved currents for scalar-tensor Horndeski theory

NASA Astrophysics Data System (ADS)

Schmidt, J.; Bičák, J.

2018-04-01

The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity, we extend these methods to the general Horndeski theory and find the covariant conserved currents for all four Lagrangians. The current is also constructed in the case of linear perturbations involving both metric and scalar fields. As a specific illustration, we derive a superpotential that leads to the covariantly conserved current in the Branse-Dicke theory.

Covariant electrodynamics in linear media: Optical metric

NASA Astrophysics Data System (ADS)

Thompson, Robert T.

2018-03-01

While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance—form invariance under general coordinate transformations, including between accelerating frames—that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framework for electrodynamics in general dielectric media residing in curved background space-times. In particular, I derive a relation for the spatial medium parameters measured by an arbitrary timelike observer. In terms of those medium parameters I derive an explicit expression for the pseudo-Finslerian optical metric of birefringent media and show how it reduces to a pseudo-Riemannian optical metric for nonbirefringent media. This formulation provides a basis for a unified approach to ray and congruence tracing through media in curved space-times that may smoothly vary among positively refracting, negatively refracting, and vacuum.

Nonparametric tests for interaction and group differences in a two-way layout.

PubMed

Fisher, A C; Wallenstein, S

1991-01-01

Nonparametric tests of group differences and interaction across strata are developed in which the null hypotheses for these tests are expressed as functions of rho i = P(X > Y) + 1/2P(X = Y), where X refers to a random observation from one group and Y refers to a random observation from the other group within stratum i. The estimator r of the parameter rho is shown to be a useful way to summarize and examine data for ordinal and continuous data.

Earth Observing System Covariance Realism Updates

NASA Technical Reports Server (NTRS)

Ojeda Romero, Juan A.; Miguel, Fred

2017-01-01

This presentation will be given at the International Earth Science Constellation Mission Operations Working Group meetings June 13-15, 2017 to discuss the Earth Observing System Covariance Realism updates.

Evaluation of energy balance closure adjustment methods by independent evapotranspiration estimates from lysimeters and hydrological simulations

DOE PAGES

Mauder, Matthias; Genzel, Sandra; Fu, Jin; ...

2017-11-10

Here, we report non-closure of the surface energy balance is a frequently observed phenomenon of hydrometeorological field measurements, when using the eddy-covariance method, which can be ascribed to an underestimation of the turbulent fluxes. Several approaches have been proposed in order to adjust the measured fluxes for this apparent systematic error. However, there are uncertainties about partitioning of the energy balance residual between the sensible and latent heat flux and whether such a correction should be applied on 30-minute data or longer time scales. The data for this study originate from two grassland sites in southern Germany, where measurements frommore » weighable lysimeters are available as reference. The adjusted evapotranspiration rates are also compared with joint energy and water balance simulations using a physically-based distributed hydrological model. We evaluate two adjustment methods: the first one preserves the Bowen ratio and the correction factor is determined on a daily basis. The second one attributes a smaller portion of the residual energy to the latent heat flux than to the sensible heat flux for closing the energy balance for every 30-minute flux integration interval. Both methods lead to an improved agreement of the eddy-covariance based fluxes with the independent lysimeter estimates and the physically-based model simulations. The first method results in a better comparability of evapotranspiration rates, and the second method leads to a smaller overall bias. These results are similar between both sites despite considerable differences in terrain complexity and grassland management. Moreover, we found that a daily adjustment factor leads to less scatter than a complete partitioning of the residual for every half-hour time interval. Lastly, the vertical temperature gradient in the surface layer and friction velocity were identified as important predictors for a potential future parameterization of the energy balance

Evaluation of energy balance closure adjustment methods by independent evapotranspiration estimates from lysimeters and hydrological simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mauder, Matthias; Genzel, Sandra; Fu, Jin

Here, we report non-closure of the surface energy balance is a frequently observed phenomenon of hydrometeorological field measurements, when using the eddy-covariance method, which can be ascribed to an underestimation of the turbulent fluxes. Several approaches have been proposed in order to adjust the measured fluxes for this apparent systematic error. However, there are uncertainties about partitioning of the energy balance residual between the sensible and latent heat flux and whether such a correction should be applied on 30-minute data or longer time scales. The data for this study originate from two grassland sites in southern Germany, where measurements frommore » weighable lysimeters are available as reference. The adjusted evapotranspiration rates are also compared with joint energy and water balance simulations using a physically-based distributed hydrological model. We evaluate two adjustment methods: the first one preserves the Bowen ratio and the correction factor is determined on a daily basis. The second one attributes a smaller portion of the residual energy to the latent heat flux than to the sensible heat flux for closing the energy balance for every 30-minute flux integration interval. Both methods lead to an improved agreement of the eddy-covariance based fluxes with the independent lysimeter estimates and the physically-based model simulations. The first method results in a better comparability of evapotranspiration rates, and the second method leads to a smaller overall bias. These results are similar between both sites despite considerable differences in terrain complexity and grassland management. Moreover, we found that a daily adjustment factor leads to less scatter than a complete partitioning of the residual for every half-hour time interval. Lastly, the vertical temperature gradient in the surface layer and friction velocity were identified as important predictors for a potential future parameterization of the energy balance

A Class of Population Covariance Matrices in the Bootstrap Approach to Covariance Structure Analysis

ERIC Educational Resources Information Center

Yuan, Ke-Hai; Hayashi, Kentaro; Yanagihara, Hirokazu

2007-01-01

Model evaluation in covariance structure analysis is critical before the results can be trusted. Due to finite sample sizes and unknown distributions of real data, existing conclusions regarding a particular statistic may not be applicable in practice. The bootstrap procedure automatically takes care of the unknown distribution and, for a given…

Separating the Air Quality Impact of a Major Highway and Nearby Sources by Nonparametric Trajectory Analysis

EPA Science Inventory

Nonparametric Trajectory Analysis (NTA), a receptor-oriented model, was used to assess the impact of local sources of air pollution at monitoring sites located adjacent to highway I-15 in Las Vegas, NV. Measurements of black carbon, carbon monoxide, nitrogen oxides, and sulfur di...

Autism-specific covariation in perceptual performances: "g" or "p" factor?

PubMed

Meilleur, Andrée-Anne S; Berthiaume, Claude; Bertone, Armando; Mottron, Laurent

2014-01-01

Autistic perception is characterized by atypical and sometimes exceptional performance in several low- (e.g., discrimination) and mid-level (e.g., pattern matching) tasks in both visual and auditory domains. A factor that specifically affects perceptive abilities in autistic individuals should manifest as an autism-specific association between perceptual tasks. The first purpose of this study was to explore how perceptual performances are associated within or across processing levels and/or modalities. The second purpose was to determine if general intelligence, the major factor that accounts for covariation in task performances in non-autistic individuals, equally controls perceptual abilities in autistic individuals. We asked 46 autistic individuals and 46 typically developing controls to perform four tasks measuring low- or mid-level visual or auditory processing. Intelligence was measured with the Wechsler's Intelligence Scale (FSIQ) and Raven Progressive Matrices (RPM). We conducted linear regression models to compare task performances between groups and patterns of covariation between tasks. The addition of either Wechsler's FSIQ or RPM in the regression models controlled for the effects of intelligence. In typically developing individuals, most perceptual tasks were associated with intelligence measured either by RPM or Wechsler FSIQ. The residual covariation between unimodal tasks, i.e. covariation not explained by intelligence, could be explained by a modality-specific factor. In the autistic group, residual covariation revealed the presence of a plurimodal factor specific to autism. Autistic individuals show exceptional performance in some perceptual tasks. Here, we demonstrate the existence of specific, plurimodal covariation that does not dependent on general intelligence (or "g" factor). Instead, this residual covariation is accounted for by a common perceptual process (or "p" factor), which may drive perceptual abilities differently in autistic and

Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem*

PubMed Central

Katsevich, E.; Katsevich, A.; Singer, A.

2015-01-01

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy two-dimensional projection images taken at unknown directions to reconstruct the three-dimensional (3D) structure of the molecule. In some situations, the molecule under examination exhibits structural variability, which poses a fundamental challenge in SPR. The heterogeneity problem is the task of mapping the space of conformational states of a molecule. It has been previously suggested that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem. Estimating the covariance matrix is challenging, since only projections of the molecules are observed, but not the molecules themselves. In this paper, we formulate a general problem of covariance estimation from noisy projections of samples. This problem has intimate connections with matrix completion problems and high-dimensional principal component analysis. We propose an estimator and prove its consistency. When there are finitely many heterogeneity classes, the spectrum of the estimated covariance matrix reveals the number of classes. The estimator can be found as the solution to a certain linear system. In the cryo-EM case, the linear operator to be inverted, which we term the projection covariance transform, is an important object in covariance estimation for tomographic problems involving structural variation. Inverting it involves applying a filter akin to the ramp filter in tomography. We design a basis in which this linear operator is sparse and thus can be tractably inverted despite its large size. We demonstrate via numerical experiments on synthetic datasets the robustness of our algorithm to high levels of noise. PMID:25699132

Parametrically Guided Generalized Additive Models with Application to Mergers and Acquisitions Data.

PubMed

Fan, Jianqing; Maity, Arnab; Wang, Yihui; Wu, Yichao

2013-01-01

Generalized nonparametric additive models present a flexible way to evaluate the effects of several covariates on a general outcome of interest via a link function. In this modeling framework, one assumes that the effect of each of the covariates is nonparametric and additive. However, in practice, often there is prior information available about the shape of the regression functions, possibly from pilot studies or exploratory analysis. In this paper, we consider such situations and propose an estimation procedure where the prior information is used as a parametric guide to fit the additive model. Specifically, we first posit a parametric family for each of the regression functions using the prior information (parametric guides). After removing these parametric trends, we then estimate the remainder of the nonparametric functions using a nonparametric generalized additive model, and form the final estimates by adding back the parametric trend. We investigate the asymptotic properties of the estimates and show that when a good guide is chosen, the asymptotic variance of the estimates can be reduced significantly while keeping the asymptotic variance same as the unguided estimator. We observe the performance of our method via a simulation study and demonstrate our method by applying to a real data set on mergers and acquisitions.

Parametrically Guided Generalized Additive Models with Application to Mergers and Acquisitions Data

PubMed Central

Fan, Jianqing; Maity, Arnab; Wang, Yihui; Wu, Yichao

2012-01-01

Generalized nonparametric additive models present a flexible way to evaluate the effects of several covariates on a general outcome of interest via a link function. In this modeling framework, one assumes that the effect of each of the covariates is nonparametric and additive. However, in practice, often there is prior information available about the shape of the regression functions, possibly from pilot studies or exploratory analysis. In this paper, we consider such situations and propose an estimation procedure where the prior information is used as a parametric guide to fit the additive model. Specifically, we first posit a parametric family for each of the regression functions using the prior information (parametric guides). After removing these parametric trends, we then estimate the remainder of the nonparametric functions using a nonparametric generalized additive model, and form the final estimates by adding back the parametric trend. We investigate the asymptotic properties of the estimates and show that when a good guide is chosen, the asymptotic variance of the estimates can be reduced significantly while keeping the asymptotic variance same as the unguided estimator. We observe the performance of our method via a simulation study and demonstrate our method by applying to a real data set on mergers and acquisitions. PMID:23645976

A Nonparametric Test for Homogeneity of Variances: Application to GPAs of Students across Academic Majors

ERIC Educational Resources Information Center

Bakir, Saad T.

2010-01-01

We propose a nonparametric (or distribution-free) procedure for testing the equality of several population variances (or scale parameters). The proposed test is a modification of Bakir's (1989, Commun. Statist., Simul-Comp., 18, 757-775) analysis of means by ranks (ANOMR) procedure for testing the equality of several population means. A proof is…

Beamforming using subspace estimation from a diagonally averaged sample covariance.

PubMed

Quijano, Jorge E; Zurk, Lisa M

2017-08-01

The potential benefit of a large-aperture sonar array for high resolution target localization is often challenged by the lack of sufficient data required for adaptive beamforming. This paper introduces a Toeplitz-constrained estimator of the clairvoyant signal covariance matrix corresponding to multiple far-field targets embedded in background isotropic noise. The estimator is obtained by averaging along subdiagonals of the sample covariance matrix, followed by covariance extrapolation using the method of maximum entropy. The sample covariance is computed from limited data snapshots, a situation commonly encountered with large-aperture arrays in environments characterized by short periods of local stationarity. Eigenvectors computed from the Toeplitz-constrained covariance are used to construct signal-subspace projector matrices, which are shown to reduce background noise and improve detection of closely spaced targets when applied to subspace beamforming. Monte Carlo simulations corresponding to increasing array aperture suggest convergence of the proposed projector to the clairvoyant signal projector, thereby outperforming the classic projector obtained from the sample eigenvectors. Beamforming performance of the proposed method is analyzed using simulated data, as well as experimental data from the Shallow Water Array Performance experiment.

Shrinkage Estimation of Varying Covariate Effects Based On Quantile Regression

PubMed Central

Peng, Limin; Xu, Jinfeng; Kutner, Nancy

2013-01-01

Varying covariate effects often manifest meaningful heterogeneity in covariate-response associations. In this paper, we adopt a quantile regression model that assumes linearity at a continuous range of quantile levels as a tool to explore such data dynamics. The consideration of potential non-constancy of covariate effects necessitates a new perspective for variable selection, which, under the assumed quantile regression model, is to retain variables that have effects on all quantiles of interest as well as those that influence only part of quantiles considered. Current work on l1-penalized quantile regression either does not concern varying covariate effects or may not produce consistent variable selection in the presence of covariates with partial effects, a practical scenario of interest. In this work, we propose a shrinkage approach by adopting a novel uniform adaptive LASSO penalty. The new approach enjoys easy implementation without requiring smoothing. Moreover, it can consistently identify the true model (uniformly across quantiles) and achieve the oracle estimation efficiency. We further extend the proposed shrinkage method to the case where responses are subject to random right censoring. Numerical studies confirm the theoretical results and support the utility of our proposals. PMID:25332515

Triangular covariance factorizations for. Ph.D. Thesis. - Calif. Univ.

NASA Technical Reports Server (NTRS)

Thornton, C. L.

1976-01-01

An improved computational form of the discrete Kalman filter is derived using an upper triangular factorization of the error covariance matrix. The covariance P is factored such that P = UDUT where U is unit upper triangular and D is diagonal. Recursions are developed for propagating the U-D covariance factors together with the corresponding state estimate. The resulting algorithm, referred to as the U-D filter, combines the superior numerical precision of square root filtering techniques with an efficiency comparable to that of Kalman's original formula. Moreover, this method is easily implemented and involves no more computer storage than the Kalman algorithm. These characteristics make the U-D method an attractive realtime filtering technique. A new covariance error analysis technique is obtained from an extension of the U-D filter equations. This evaluation method is flexible and efficient and may provide significantly improved numerical results. Cost comparisons show that for a large class of problems the U-D evaluation algorithm is noticeably less expensive than conventional error analysis methods.

Video based object representation and classification using multiple covariance matrices.

PubMed

Zhang, Yurong; Liu, Quan

2017-01-01

Video based object recognition and classification has been widely studied in computer vision and image processing area. One main issue of this task is to develop an effective representation for video. This problem can generally be formulated as image set representation. In this paper, we present a new method called Multiple Covariance Discriminative Learning (MCDL) for image set representation and classification problem. The core idea of MCDL is to represent an image set using multiple covariance matrices with each covariance matrix representing one cluster of images. Firstly, we use the Nonnegative Matrix Factorization (NMF) method to do image clustering within each image set, and then adopt Covariance Discriminative Learning on each cluster (subset) of images. At last, we adopt KLDA and nearest neighborhood classification method for image set classification. Promising experimental results on several datasets show the effectiveness of our MCDL method.

The utility of covariance of combining ability in plant breeding.

PubMed

Arunachalam, V

1976-11-01

The definition of covariances of half- and full sibs, and hence that of variances of general and specific combining ability with regard to a quantitative character, is extended to take into account the respective covariances between a pair of characters. The interpretation of the dispersion and correlation matrices of general and specific combining ability is discussed by considering a set of single, three- and four-way crosses, made using diallel and line × tester mating systems in Pennisetum typhoides. The general implications of the concept of covariance of combining ability in plant breeding are discussed.

Bayesian Analysis of Structural Equation Models with Nonlinear Covariates and Latent Variables

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2006-01-01

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…

To Covary or Not to Covary, That is the Question

NASA Astrophysics Data System (ADS)

Oehlert, A. M.; Swart, P. K.

2016-12-01

The meaning of covariation between the δ13C values of carbonate carbon and that of organic material is classically interpreted as reflecting original variations in the δ13C values of the dissolved inorganic carbon in the depositional environment. However, recently it has been shown by the examination of a core from Great Bahama Bank (Clino) that during exposure not only do the rocks become altered acquiring a negative δ13C value, but at the same time terrestrial vegetation adds organic carbon to the system masking the original marine values. These processes yield a strong positive covariation between δ13Corg and δ13Ccar values even though the signals are clearly not original and unrelated to the marine δ13C values. Examining the correlation between the organic and inorganic system in a stratigraphic sense at Clino and in a second more proximally located core (Unda) using a windowed correlation coefficient technique reveals that the correlation is even more complex. Changes in slope and the magnitude of the correlation are associated with exposure surfaces, facies changes, dolomitized bodies, and non-depositional surfaces. Finally other isotopic systems such as the δ13C value of specific organic compounds as well as δ15N values of bulk and individual compounds can provide additional information. In the case of δ15N values, decreases reflect a changes in the influence of terrestrial organic material and an increase contribution of organic material from the platform surface where the main source of nitrogen is derived from the activities of cyanobacteria.

A Comparison of Methods for Estimating the Determinant of High-Dimensional Covariance Matrix.

PubMed

Hu, Zongliang; Dong, Kai; Dai, Wenlin; Tong, Tiejun

2017-09-21

The determinant of the covariance matrix for high-dimensional data plays an important role in statistical inference and decision. It has many real applications including statistical tests and information theory. Due to the statistical and computational challenges with high dimensionality, little work has been proposed in the literature for estimating the determinant of high-dimensional covariance matrix. In this paper, we estimate the determinant of the covariance matrix using some recent proposals for estimating high-dimensional covariance matrix. Specifically, we consider a total of eight covariance matrix estimation methods for comparison. Through extensive simulation studies, we explore and summarize some interesting comparison results among all compared methods. We also provide practical guidelines based on the sample size, the dimension, and the correlation of the data set for estimating the determinant of high-dimensional covariance matrix. Finally, from a perspective of the loss function, the comparison study in this paper may also serve as a proxy to assess the performance of the covariance matrix estimation.

Sparse Covariance Matrix Estimation With Eigenvalue Constraints

PubMed Central

LIU, Han; WANG, Lie; ZHAO, Tuo

2014-01-01

We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholding and projection algorithm based on the alternating direction method of multipliers. Empirically, we conduct thorough numerical experiments on simulated datasets as well as real data examples to illustrate the usefulness of our method. Supplementary materials for the article are available online. PMID:25620866

Competing risks models and time-dependent covariates

PubMed Central

Barnett, Adrian; Graves, Nick

2008-01-01

New statistical models for analysing survival data in an intensive care unit context have recently been developed. Two models that offer significant advantages over standard survival analyses are competing risks models and multistate models. Wolkewitz and colleagues used a competing risks model to examine survival times for nosocomial pneumonia and mortality. Their model was able to incorporate time-dependent covariates and so examine how risk factors that changed with time affected the chances of infection or death. We briefly explain how an alternative modelling technique (using logistic regression) can more fully exploit time-dependent covariates for this type of data. PMID:18423067

Diffeomorphic demons: efficient non-parametric image registration.

PubMed

Vercauteren, Tom; Pennec, Xavier; Perchant, Aymeric; Ayache, Nicholas

2009-03-01

We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. In the first part of this paper, we show that Thirion's demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.

Covariant deformed oscillator algebras

NASA Technical Reports Server (NTRS)

Quesne, Christiane

1995-01-01

The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

WAIS-IV subtest covariance structure: conceptual and statistical considerations.

PubMed

Ward, L Charles; Bergman, Maria A; Hebert, Katina R

2012-06-01

D. Wechsler (2008b) reported confirmatory factor analyses (CFAs) with standardization data (ages 16-69 years) for 10 core and 5 supplemental subtests from the Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV). Analyses of the 15 subtests supported 4 hypothesized oblique factors (Verbal Comprehension, Working Memory, Perceptual Reasoning, and Processing Speed) but also revealed unexplained covariance between Block Design and Visual Puzzles (Perceptual Reasoning subtests). That covariance was not included in the final models. Instead, a path was added from Working Memory to Figure Weights (Perceptual Reasoning subtest) to improve fit and achieve a desired factor pattern. The present research with the same data (N = 1,800) showed that the path from Working Memory to Figure Weights increases the association between Working Memory and Matrix Reasoning. Specifying both paths improves model fit and largely eliminates unexplained covariance between Block Design and Visual Puzzles but with the undesirable consequence that Figure Weights and Matrix Reasoning are equally determined by Perceptual Reasoning and Working Memory. An alternative 4-factor model was proposed that explained theory-implied covariance between Block Design and Visual Puzzles and between Arithmetic and Figure Weights while maintaining compatibility with WAIS-IV Index structure. The proposed model compared favorably with a 5-factor model based on Cattell-Horn-Carroll theory. The present findings emphasize that covariance model comparisons should involve considerations of conceptual coherence and theoretical adherence in addition to statistical fit. (c) 2012 APA, all rights reserved

Explicitly covariant dispersion relations and self-induced transparency

NASA Astrophysics Data System (ADS)

Mahajan, S. M.; Asenjo, Felipe A.

2017-02-01

Explicitly covariant dispersion relations for a variety of plasma waves in unmagnetized and magnetized plasmas are derived in a systematic manner from a fully covariant plasma formulation. One needs to invoke relatively little known invariant combinations constructed from the ambient electromagnetic fields and the wave vector to accomplish the program. The implication of this work applied to the self-induced transparency effect is discussed. Some problems arising from the inconsistent use of relativity are pointed out.

Genetic covariance between central corneal thickness and anterior chamber volume: a Hungarian twin study.

PubMed

Toth, Georgina Zsofia; Racz, Adel; Tarnoki, Adam Domonkos; Tarnoki, David Laszlo; Szekelyhidi, Zita; Littvay, Levente; Suveges, Ildiko; Nemeth, Janos; Nagy, Zoltan Zsolt

2014-10-01

Few, and inconsistent, studies have showed high heritability of some parameters of the anterior segment of the eye; however, no heritability of anterior chamber volume (ACV) has been reported, and no study has been performed to investigate the correlation between the ACV and central corneal thickness (CCT). Anterior segment measurements (Pentacam, Oculus) were obtained from 220 eyes of 110 adult Hungarian twins (41 monozygotic and 14 same-sex dizygotic pairs; 80% women; age 48.6 ± 15.5 years) obtained from the Hungarian Twin Registry. Age- and sex-adjusted heritability of ACV was 85% (bootstrapped 95% confidence interval; CI: 69% to 93%), and 88% for CCT (CI: 79% to 95%). Common environmental effects had no influence, and unshared environmental factors were responsible for 12% and 15% of the variance, respectively. The correlation between ACV and CCT was negative and significant (r ph = -0.35, p < .05), and genetic factors accounted for the covariance significantly (0.934; CI: 0.418, 1.061) based on the bivariate Cholesky decomposition model. These findings support the high heritability of ACV and central corneal thickness, and a strong genetic covariance between them, which underscores the importance of identification of the specific genetic factors and the family risk-based screening of disorders related to these variables, such as open-angle and also angle closure glaucoma and corneal endothelial alterations.

Further Empirical Results on Parametric Versus Non-Parametric IRT Modeling of Likert-Type Personality Data

ERIC Educational Resources Information Center

Maydeu-Olivares, Albert

2005-01-01

Chernyshenko, Stark, Chan, Drasgow, and Williams (2001) investigated the fit of Samejima's logistic graded model and Levine's non-parametric MFS model to the scales of two personality questionnaires and found that the graded model did not fit well. We attribute the poor fit of the graded model to small amounts of multidimensionality present in…

Super-sample covariance approximations and partial sky coverage

NASA Astrophysics Data System (ADS)

Lacasa, Fabien; Lima, Marcos; Aguena, Michel

2018-04-01

Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.

Triangles in ROC space: History and theory of "nonparametric" measures of sensitivity and response bias.

PubMed

Macmillan, N A; Creelman, C D

1996-06-01

Can accuracy and response bias in two-stimulus, two-response recognition or detection experiments be measured nonparametrically? Pollack and Norman (1964) answered this question affirmatively for sensitivity, Hodos (1970) for bias: Both proposed measures based on triangular areas in receiver-operating characteristic space. Their papers, and especially a paper by Grier (1971) that provided computing formulas for the measures, continue to be heavily cited in a wide range of content areas. In our sample of articles, most authors described triangle-based measures as making fewer assumptions than measures associated with detection theory. However, we show that statistics based on products or ratios of right triangle areas, including a recently proposed bias index and a not-yetproposed but apparently plausible sensitivity index, are consistent with a decision process based on logistic distributions. Even the Pollack and Norman measure, which is based on non-right triangles, is approximately logistic for low values of sensitivity. Simple geometric models for sensitivity and bias are not nonparametric, even if their implications are not acknowledged in the defining publications.

Uranium Associations with Kidney Outcomes Vary by Urine Concentration Adjustment Method

PubMed Central

Shelley, Rebecca; Kim, Nam-Soo; Parsons, Patrick J.; Lee, Byung-Kook; Agnew, Jacqueline; Jaar, Bernard G.; Steuerwald, Amy J.; Matanoski, Genevieve; Fadrowski, Jeffrey; Schwartz, Brian S.; Todd, Andrew C.; Simon, David; Weaver, Virginia M.

2017-01-01

Uranium is a ubiquitous metal that is nephrotoxic at high doses. Few epidemiologic studies have examined the kidney filtration impact of chronic environmental exposure. In 684 lead workers environmentally exposed to uranium, multiple linear regression was used to examine associations of uranium measured in a four-hour urine collection with measured creatinine clearance, serum creatinine- and cystatin-C-based estimated glomerular filtration rates, and N-acetyl-β-D-glucosaminidase (NAG). Three methods were utilized, in separate models, to adjust uranium levels for urine concentration - μg uranium/g creatinine; μg uranium/L and urine creatinine as separate covariates; and μg uranium/4 hr. Median urine uranium levels were 0.07 μg/g creatinine and 0.02 μg/4 hr and were highly correlated (rs =0.95). After adjustment, higher ln-urine uranium was associated with lower measured creatinine clearance and higher NAG in models that used urine creatinine to adjust for urine concentration but not in models that used total uranium excreted (μg/4 hr). These results suggest that, in some instances, associations between urine toxicants and kidney outcomes may be statistical, due to the use of urine creatinine in both exposure and outcome metrics, rather than nephrotoxic. These findings support consideration of non-creatinine-based methods of adjustment for urine concentration in nephrotoxicant research. PMID:23591699

Revealing hidden covariation detection: evidence for implicit abstraction at study.

PubMed

Rossnagel, C S

2001-09-01

Four experiments in the brain scans paradigm (P. Lewicki, T. Hill, & I. Sasaki, 1989) investigated hidden covariation detection (HCD). In Experiment 1 HCD was found in an implicit- but not in an explicit-instruction group. In Experiment 2 HCD was impaired by nonholistic perception of stimuli but not by divided attention. In Experiment 3 HCD was eliminated by interspersing stimuli that deviated from the critical covariation. In Experiment 4 a transfer procedure was used. HCD was found with dissimilar test stimuli that preserved the covariation but was almost eliminated with similar stimuli that were neutral as to the covariation. Awareness was assessed both by objective and subjective tests in all experiments. Results suggest that HCD is an effect of implicit rule abstraction and that similarity processing plays only a minor role. HCD might be suppressed by intentional search strategies that induce inappropriate aggregation of stimulus information.

Covariation Neglect among Novice Investors

ERIC Educational Resources Information Center

Hedesstrom, Ted Martin; Svedsater, Henrik; Garling, Tommy

2006-01-01

In 4 experiments, undergraduates made hypothetical investment choices. In Experiment 1, participants paid more attention to the volatility of individual assets than to the volatility of aggregated portfolios. The results of Experiment 2 show that most participants diversified even when this increased risk because of covariation between the returns…

The non-parametric Parzen's window in stereo vision matching.

PubMed

Pajares, G; de la Cruz, J

2002-01-01

This paper presents an approach to the local stereovision matching problem using edge segments as features with four attributes. From these attributes we compute a matching probability between pairs of features of the stereo images. A correspondence is said true when such a probability is maximum. We introduce a nonparametric strategy based on Parzen's window (1962) to estimate a probability density function (PDF) which is used to obtain the matching probability. This is the main finding of the paper. A comparative analysis of other recent matching methods is included to show that this finding can be justified theoretically. A generalization of the proposed method is made in order to give guidelines about its use with the similarity constraint and also in different environments where other features and attributes are more suitable.

Structural Covariance of the Default Network in Healthy and Pathological Aging

PubMed Central

Turner, Gary R.

2013-01-01

Significant progress has been made uncovering functional brain networks, yet little is known about the corresponding structural covariance networks. The default network's functional architecture has been shown to change over the course of healthy and pathological aging. We examined cross-sectional and longitudinal datasets to reveal the structural covariance of the human default network across the adult lifespan and through the progression of Alzheimer's disease (AD). We used a novel approach to identify the structural covariance of the default network and derive individual participant scores that reflect the covariance pattern in each brain image. A seed-based multivariate analysis was conducted on structural images in the cross-sectional OASIS (N = 414) and longitudinal Alzheimer's Disease Neuroimaging Initiative (N = 434) datasets. We reproduced the distributed topology of the default network, based on a posterior cingulate cortex seed, consistent with prior reports of this intrinsic connectivity network. Structural covariance of the default network scores declined in healthy and pathological aging. Decline was greatest in the AD cohort and in those who progressed from mild cognitive impairment to AD. Structural covariance of the default network scores were positively associated with general cognitive status, reduced in APOEε4 carriers versus noncarriers, and associated with CSF biomarkers of AD. These findings identify the structural covariance of the default network and characterize changes to the network's gray matter integrity across the lifespan and through the progression of AD. The findings provide evidence for the large-scale network model of neurodegenerative disease, in which neurodegeneration spreads through intrinsically connected brain networks in a disease specific manner. PMID:24048852

Covariance Applications in Criticality Safety, Light Water Reactor Analysis, and Spent Fuel Characterization

DOE PAGES

Williams, M. L.; Wiarda, D.; Ilas, G.; ...

2014-06-15

Recently, we processed a new covariance data library based on ENDF/B-VII.1 for the SCALE nuclear analysis code system. The multigroup covariance data are discussed here, along with testing and application results for critical benchmark experiments. Moreover, the cross section covariance library, along with covariances for fission product yields and decay data, is used to compute uncertainties in the decay heat produced by a burned reactor fuel assembly.

Random sampling and validation of covariance matrices of resonance parameters

NASA Astrophysics Data System (ADS)

Plevnik, Lucijan; Zerovnik, Gašper

2017-09-01

Analytically exact methods for random sampling of arbitrary correlated parameters are presented. Emphasis is given on one hand on the possible inconsistencies in the covariance data, concentrating on the positive semi-definiteness and consistent sampling of correlated inherently positive parameters, and on the other hand on optimization of the implementation of the methods itself. The methods have been applied in the program ENDSAM, written in the Fortran language, which from a file from a nuclear data library of a chosen isotope in ENDF-6 format produces an arbitrary number of new files in ENDF-6 format which contain values of random samples of resonance parameters (in accordance with corresponding covariance matrices) in places of original values. The source code for the program ENDSAM is available from the OECD/NEA Data Bank. The program works in the following steps: reads resonance parameters and their covariance data from nuclear data library, checks whether the covariance data is consistent, and produces random samples of resonance parameters. The code has been validated with both realistic and artificial data to show that the produced samples are statistically consistent. Additionally, the code was used to validate covariance data in existing nuclear data libraries. A list of inconsistencies, observed in covariance data of resonance parameters in ENDF-VII.1, JEFF-3.2 and JENDL-4.0 is presented. For now, the work has been limited to resonance parameters, however the methods presented are general and can in principle be extended to sampling and validation of any nuclear data.

Nonparametric Model of Smooth Muscle Force Production During Electrical Stimulation.

PubMed

Cole, Marc; Eikenberry, Steffen; Kato, Takahide; Sandler, Roman A; Yamashiro, Stanley M; Marmarelis, Vasilis Z

2017-03-01

A nonparametric model of smooth muscle tension response to electrical stimulation was estimated using the Laguerre expansion technique of nonlinear system kernel estimation. The experimental data consisted of force responses of smooth muscle to energy-matched alternating single pulse and burst current stimuli. The burst stimuli led to at least a 10-fold increase in peak force in smooth muscle from Mytilus edulis, despite the constant energy constraint. A linear model did not fit the data. However, a second-order model fit the data accurately, so the higher-order models were not required to fit the data. Results showed that smooth muscle force response is not linearly related to the stimulation power.

The evolution of phenotypic integration: How directional selection reshapes covariation in mice

PubMed Central

Penna, Anna; Melo, Diogo; Bernardi, Sandra; Oyarzabal, Maria Inés; Marroig, Gabriel

2017-01-01

Abstract Variation is the basis for evolution, and understanding how variation can evolve is a central question in biology. In complex phenotypes, covariation plays an even more important role, as genetic associations between traits can bias and alter evolutionary change. Covariation can be shaped by complex interactions between loci, and this genetic architecture can also change during evolution. In this article, we analyzed mouse lines experimentally selected for changes in size to address the question of how multivariate covariation changes under directional selection, as well as to identify the consequences of these changes to evolution. Selected lines showed a clear restructuring of covariation in their cranium and, instead of depleting their size variation, these lines increased their magnitude of integration and the proportion of variation associated with the direction of selection. This result is compatible with recent theoretical works on the evolution of covariation that take the complexities of genetic architecture into account. This result also contradicts the traditional view of the effects of selection on available covariation and suggests a much more complex view of how populations respond to selection. PMID:28685813

Directional selection effects on patterns of phenotypic (co)variation in wild populations

PubMed Central

Patton, J. L.; Hubbe, A.; Marroig, G.

2016-01-01

Phenotypic (co)variation is a prerequisite for evolutionary change, and understanding how (co)variation evolves is of crucial importance to the biological sciences. Theoretical models predict that under directional selection, phenotypic (co)variation should evolve in step with the underlying adaptive landscape, increasing the degree of correlation among co-selected traits as well as the amount of genetic variance in the direction of selection. Whether either of these outcomes occurs in natural populations is an open question and thus an important gap in evolutionary theory. Here, we documented changes in the phenotypic (co)variation structure in two separate natural populations in each of two chipmunk species (Tamias alpinus and T. speciosus) undergoing directional selection. In populations where selection was strongest (those of T. alpinus), we observed changes, at least for one population, in phenotypic (co)variation that matched theoretical expectations, namely an increase of both phenotypic integration and (co)variance in the direction of selection and a re-alignment of the major axis of variation with the selection gradient. PMID:27881744

Directional selection effects on patterns of phenotypic (co)variation in wild populations.

PubMed

Assis, A P A; Patton, J L; Hubbe, A; Marroig, G

2016-11-30

Phenotypic (co)variation is a prerequisite for evolutionary change, and understanding how (co)variation evolves is of crucial importance to the biological sciences. Theoretical models predict that under directional selection, phenotypic (co)variation should evolve in step with the underlying adaptive landscape, increasing the degree of correlation among co-selected traits as well as the amount of genetic variance in the direction of selection. Whether either of these outcomes occurs in natural populations is an open question and thus an important gap in evolutionary theory. Here, we documented changes in the phenotypic (co)variation structure in two separate natural populations in each of two chipmunk species (Tamias alpinus and T. speciosus) undergoing directional selection. In populations where selection was strongest (those of T. alpinus), we observed changes, at least for one population, in phenotypic (co)variation that matched theoretical expectations, namely an increase of both phenotypic integration and (co)variance in the direction of selection and a re-alignment of the major axis of variation with the selection gradient. © 2016 The Author(s).

Covariate Balance in Bayesian Propensity Score Approaches for Observational Studies

ERIC Educational Resources Information Center

Chen, Jianshen; Kaplan, David

2015-01-01

Bayesian alternatives to frequentist propensity score approaches have recently been proposed. However, few studies have investigated their covariate balancing properties. This article compares a recently developed two-step Bayesian propensity score approach to the frequentist approach with respect to covariate balance. The effects of different…

Familial aggregation and linkage analysis with covariates for metabolic syndrome risk factors.

PubMed

Naseri, Parisa; Khodakarim, Soheila; Guity, Kamran; Daneshpour, Maryam S

2018-06-15

Mechanisms of metabolic syndrome (MetS) causation are complex, genetic and environmental factors are important factors for the pathogenesis of MetS In this study, we aimed to evaluate familial and genetic influences on metabolic syndrome risk factor and also assess association between FTO (rs1558902 and rs7202116) and CETP(rs1864163) genes' single nucleotide polymorphisms (SNP) with low HDL_C in the Tehran Lipid and Glucose Study (TLGS). The design was a cross-sectional study of 1776 members of 227 randomly-ascertained families. Selected families contained at least one affected metabolic syndrome and at least two members of the family had suffered a loss of HDL_C according to ATP III criteria. In this study, after confirming the familial aggregation with intra-trait correlation coefficients (ICC) of Metabolic syndrome (MetS) and the quantitative lipid traits, the genetic linkage analysis of HDL_C was performed using conditional logistic method with adjusted sex and age. The results of the aggregation analysis revealed a higher correlation between siblings than between parent-offspring pairs representing the role of genetic factors in MetS. In addition, the conditional logistic model with covariates showed that the linkage results between HDL_C and three marker, rs1558902, rs7202116 and rs1864163 were significant. In summary, a high risk of MetS was found in siblings confirming the genetic influences of metabolic syndrome risk factor. Moreover, the power to detect linkage increases in the one parameter conditional logistic model regarding the use of age and sex as covariates. Copyright © 2018. Published by Elsevier B.V.

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance

PubMed Central

Zheng, Binqi; Yuan, Xiaobing

2018-01-01

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results. PMID:29518960

A Robust Adaptive Unscented Kalman Filter for Nonlinear Estimation with Uncertain Noise Covariance.

PubMed

Zheng, Binqi; Fu, Pengcheng; Li, Baoqing; Yuan, Xiaobing

2018-03-07

The Unscented Kalman filter (UKF) may suffer from performance degradation and even divergence while mismatch between the noise distribution assumed as a priori by users and the actual ones in a real nonlinear system. To resolve this problem, this paper proposes a robust adaptive UKF (RAUKF) to improve the accuracy and robustness of state estimation with uncertain noise covariance. More specifically, at each timestep, a standard UKF will be implemented first to obtain the state estimations using the new acquired measurement data. Then an online fault-detection mechanism is adopted to judge if it is necessary to update current noise covariance. If necessary, innovation-based method and residual-based method are used to calculate the estimations of current noise covariance of process and measurement, respectively. By utilizing a weighting factor, the filter will combine the last noise covariance matrices with the estimations as the new noise covariance matrices. Finally, the state estimations will be corrected according to the new noise covariance matrices and previous state estimations. Compared with the standard UKF and other adaptive UKF algorithms, RAUKF converges faster to the actual noise covariance and thus achieves a better performance in terms of robustness, accuracy, and computation for nonlinear estimation with uncertain noise covariance, which is demonstrated by the simulation results.

The Impact of Ignoring the Level of Nesting Structure in Nonparametric Multilevel Latent Class Models

ERIC Educational Resources Information Center

Park, Jungkyu; Yu, Hsiu-Ting

2016-01-01

The multilevel latent class model (MLCM) is a multilevel extension of a latent class model (LCM) that is used to analyze nested structure data structure. The nonparametric version of an MLCM assumes a discrete latent variable at a higher-level nesting structure to account for the dependency among observations nested within a higher-level unit. In…

Probit vs. semi-nonparametric estimation: examining the role of disability on institutional entry for older adults.

PubMed

Sharma, Andy

2017-06-01

The purpose of this study was to showcase an advanced methodological approach to model disability and institutional entry. Both of these are important areas to investigate given the on-going aging of the United States population. By 2020, approximately 15% of the population will be 65 years and older. Many of these older adults will experience disability and require formal care. A probit analysis was employed to determine which disabilities were associated with admission into an institution (i.e. long-term care). Since this framework imposes strong distributional assumptions, misspecification leads to inconsistent estimators. To overcome such a short-coming, this analysis extended the probit framework by employing an advanced semi-nonparamertic maximum likelihood estimation utilizing Hermite polynomial expansions. Specification tests show semi-nonparametric estimation is preferred over probit. In terms of the estimates, semi-nonparametric ratios equal 42 for cognitive difficulty, 64 for independent living, and 111 for self-care disability while probit yields much smaller estimates of 19, 30, and 44, respectively. Public health professionals can use these results to better understand why certain interventions have not shown promise. Equally important, healthcare workers can use this research to evaluate which type of treatment plans may delay institutionalization and improve the quality of life for older adults. Implications for rehabilitation With on-going global aging, understanding the association between disability and institutional entry is important in devising successful rehabilitation interventions. Semi-nonparametric is preferred to probit and shows ambulatory and cognitive impairments present high risk for institutional entry (long-term care). Informal caregiving and home-based care require further examination as forms of rehabilitation/therapy for certain types of disabilities.

Phenotypic Covariation and Morphological Diversification in the Ruminant Skull.

PubMed

Haber, Annat

2016-05-01

Differences among clades in their diversification patterns result from a combination of extrinsic and intrinsic factors. In this study, I examined the role of intrinsic factors in the morphological diversification of ruminants, in general, and in the differences between bovids and cervids, in particular. Using skull morphology, which embodies many of the adaptations that distinguish bovids and cervids, I examined 132 of the 200 extant ruminant species. As a proxy for intrinsic constraints, I quantified different aspects of the phenotypic covariation structure within species and compared them with the among-species divergence patterns, using phylogenetic comparative methods. My results show that for most species, divergence is well aligned with their phenotypic covariance matrix and that those that are better aligned have diverged further away from their ancestor. Bovids have dispersed into a wider range of directions in morphospace than cervids, and their overall disparity is higher. This difference is best explained by the lower eccentricity of bovids' within-species covariance matrices. These results are consistent with the role of intrinsic constraints in determining amount, range, and direction of dispersion and demonstrate that intrinsic constraints can influence macroevolutionary patterns even as the covariance structure evolves.

Realistic Covariance Prediction for the Earth Science Constellation

NASA Technical Reports Server (NTRS)

Duncan, Matthew; Long, Anne

2006-01-01

Routine satellite operations for the Earth Science Constellation (ESC) include collision risk assessment between members of the constellation and other orbiting space objects. One component of the risk assessment process is computing the collision probability between two space objects. The collision probability is computed using Monte Carlo techniques as well as by numerically integrating relative state probability density functions. Each algorithm takes as inputs state vector and state vector uncertainty information for both objects. The state vector uncertainty information is expressed in terms of a covariance matrix. The collision probability computation is only as good as the inputs. Therefore, to obtain a collision calculation that is a useful decision-making metric, realistic covariance matrices must be used as inputs to the calculation. This paper describes the process used by the NASA/Goddard Space Flight Center's Earth Science Mission Operations Project to generate realistic covariance predictions for three of the Earth Science Constellation satellites: Aqua, Aura and Terra.

Handling Correlations between Covariates and Random Slopes in Multilevel Models

ERIC Educational Resources Information Center

Bates, Michael David; Castellano, Katherine E.; Rabe-Hesketh, Sophia; Skrondal, Anders

2014-01-01

This article discusses estimation of multilevel/hierarchical linear models that include cluster-level random intercepts and random slopes. Viewing the models as structural, the random intercepts and slopes represent the effects of omitted cluster-level covariates that may be correlated with included covariates. The resulting correlations between…

LOCATING NEARBY SOURCES OF AIR POLLUTION BY NONPARAMETRIC REGRESSION OF ATMOSPHERIC CONCENTRATIONS ON WIND DIRECTION. (R826238)

EPA Science Inventory

The relationship of the concentration of air pollutants to wind direction has been determined by nonparametric regression using a Gaussian kernel. The results are smooth curves with error bars that allow for the accurate determination of the wind direction where the concentrat...

Social adjustment and repressive adaptive style in survivors of pediatric cancer.

PubMed

Schulte, Fiona; Wurz, Amanda; Russell, K Brooke; Reynolds, Kathleen; Strother, Douglas; Dewey, Deborah

2018-01-01

The aim of the study was to explore the relationship between repressive adaptive style and self-reports of social adjustment in survivors of pediatric cancer compared to their siblings. We hypothesized that there would be a greater proportion of repressors among survivors of pediatric cancer compared to siblings, and that repressive adaptive style would be significantly associated with more positive self-reports of social adjustment. We utilized a cross-sectional approach. Seventy-seven families participated. Survivors of pediatric cancer (n = 77, 48% male; 8-18 years of age) and one sibling (n = 50, 48% male; 8-18 years of age) completed measures assessing repressive adaptive style and social adjustment. As well, one parent from each family completed a socio-demographic questionnaire. Questionnaire packages were mailed to eligible families who agreed to participate, and were mailed back to investigators in a pre-addressed, pre-stamped envelope. Chi-square analyses revealed there was no significant difference in the proportion of repressors among survivors and siblings. Social adjustment scores were subjected to a two (group: survivor, sibling) by two (repressor, nonrepressor) ANCOVA with gender and age as covariates. There was a significant main effect of repressive adaptive style (F = 5.69, p < .05, η 2 = 0.05) with a modest effect. Survivors and siblings with a repressive style reported significantly higher social adjustment scores (M = 106.91, SD = 11.69) compared to nonrepressors (M = 99.57, SD = 13.45). Repressive adaptive style explains some of the variance in survivors and siblings' self-reports of social adjustment. Future research should aim to better understand the role of the repressive adaptive style in survivors and siblings of children with cancer.

Preoperative psychological adjustment and surgical outcome are determinants of psychosocial status after anterior temporal lobectomy.

PubMed Central

Hermann, B P; Wyler, A R; Somes, G

1992-01-01

This investigation evaluated the role of preoperative psychological adjustment, degree of postoperative seizure reduction, and other relevant variables (age, education, IQ, age at onset of epilepsy, laterality of resection) in determining emotional/psychosocial outcome following anterior temporal lobectomy. Ninety seven patients with complex partial seizures of temporal lobe origin were administered the Minnesota Multiphasic Personality Inventory (MMPI), Washington Psychosocial Seizure Inventory (WPSI), and the General Health Questionnaire (GHQ) both before and six to eight months after anterior temporal lobectomy. The data were subjected to a nonparametric rank sum technique (O'Brien's procedure) which combined the test scores to form a single outcome index (TOTAL PSYCHOSOCIAL OUTCOME) that was analysed by multiple regression procedures. Results indicated that the most powerful predictors of patients' overall postoperative psychosocial outcome were: 1) The adequacy of their preoperative psychosocial adjustment, and 2) A totally seizure-free outcome. Additional analyses were carried out separately on the MMPI, WPSI, and GHQ to determine whether findings varied as a function of the specific outcome measure. These results were related to the larger literature concerned with the psychological outcome of anterior temporal lobectomy. PMID:1619418

Variations of cosmic large-scale structure covariance matrices across parameter space

NASA Astrophysics Data System (ADS)

Reischke, Robert; Kiessling, Alina; Schäfer, Björn Malte

2017-03-01

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the non-linear evolution of the cosmic web. As highly non-linear clustering to date has only been described by numerical N-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work, we describe the change of the matter covariance and the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from non-linear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations, we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to ℓ ≤ 1300. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimizing interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

Structural Covariance Networks in Children with Autism or ADHD

PubMed Central

Romero-Garcia, R.; Mak, E.; Bullmore, E. T.; Baron-Cohen, S.

2017-01-01

Abstract Background While autism and attention-deficit/hyperactivity disorder (ADHD) are considered distinct conditions from a diagnostic perspective, clinically they share some phenotypic features and have high comorbidity. Regardless, most studies have focused on only one condition, with considerable heterogeneity in their results. Taking a dual-condition approach might help elucidate shared and distinct neural characteristics. Method Graph theory was used to analyse topological properties of structural covariance networks across both conditions and relative to a neurotypical (NT; n = 87) group using data from the ABIDE (autism; n = 62) and ADHD-200 datasets (ADHD; n = 69). Regional cortical thickness was used to construct the structural covariance networks. This was analysed in a theoretical framework examining potential differences in long and short-range connectivity, with a specific focus on relation between central graph measures and cortical thickness. Results We found convergence between autism and ADHD, where both conditions show an overall decrease in CT covariance with increased Euclidean distance between centroids compared with a NT population. The 2 conditions also show divergence. Namely, there is less modular overlap between the 2 conditions than there is between each condition and the NT group. The ADHD group also showed reduced cortical thickness and lower degree in hub regions than the autism group. Lastly, the ADHD group also showed reduced wiring costs compared with the autism groups. Conclusions Our results indicate a need for taking an integrated approach when considering highly comorbid conditions such as autism and ADHD. Furthermore, autism and ADHD both showed alterations in the relation between inter-regional covariance and centroid distance, where both groups show a steeper decline in covariance as a function of distance. The 2 groups also diverge on modular organization, cortical thickness of hub regions and wiring cost of the

Structural Covariance Networks in Children with Autism or ADHD.

PubMed

Bethlehem, R A I; Romero-Garcia, R; Mak, E; Bullmore, E T; Baron-Cohen, S

2017-08-01

While autism and attention-deficit/hyperactivity disorder (ADHD) are considered distinct conditions from a diagnostic perspective, clinically they share some phenotypic features and have high comorbidity. Regardless, most studies have focused on only one condition, with considerable heterogeneity in their results. Taking a dual-condition approach might help elucidate shared and distinct neural characteristics. Graph theory was used to analyse topological properties of structural covariance networks across both conditions and relative to a neurotypical (NT; n = 87) group using data from the ABIDE (autism; n = 62) and ADHD-200 datasets (ADHD; n = 69). Regional cortical thickness was used to construct the structural covariance networks. This was analysed in a theoretical framework examining potential differences in long and short-range connectivity, with a specific focus on relation between central graph measures and cortical thickness. We found convergence between autism and ADHD, where both conditions show an overall decrease in CT covariance with increased Euclidean distance between centroids compared with a NT population. The 2 conditions also show divergence. Namely, there is less modular overlap between the 2 conditions than there is between each condition and the NT group. The ADHD group also showed reduced cortical thickness and lower degree in hub regions than the autism group. Lastly, the ADHD group also showed reduced wiring costs compared with the autism groups. Our results indicate a need for taking an integrated approach when considering highly comorbid conditions such as autism and ADHD. Furthermore, autism and ADHD both showed alterations in the relation between inter-regional covariance and centroid distance, where both groups show a steeper decline in covariance as a function of distance. The 2 groups also diverge on modular organization, cortical thickness of hub regions and wiring cost of the covariance network. Thus, on some network features the

Genome-Wide Networks of Amino Acid Covariances Are Common among Viruses

PubMed Central

Donlin, Maureen J.; Szeto, Brandon; Gohara, David W.; Aurora, Rajeev

2012-01-01

Coordinated variation among positions in amino acid sequence alignments can reveal genetic dependencies at noncontiguous positions, but methods to assess these interactions are incompletely developed. Previously, we found genome-wide networks of covarying residue positions in the hepatitis C virus genome (R. Aurora, M. J. Donlin, N. A. Cannon, and J. E. Tavis, J. Clin. Invest. 119:225–236, 2009). Here, we asked whether such networks are present in a diverse set of viruses and, if so, what they may imply about viral biology. Viral sequences were obtained for 16 viruses in 13 species from 9 families. The entire viral coding potential for each virus was aligned, all possible amino acid covariances were identified using the observed-minus-expected-squared algorithm at a false-discovery rate of ≤1%, and networks of covariances were assessed using standard methods. Covariances that spanned the viral coding potential were common in all viruses. In all cases, the covariances formed a single network that contained essentially all of the covariances. The hepatitis C virus networks had hub-and-spoke topologies, but all other networks had random topologies with an unusually large number of highly connected nodes. These results indicate that genome-wide networks of genetic associations and the coordinated evolution they imply are very common in viral genomes, that the networks rarely have the hub-and-spoke topology that dominates other biological networks, and that network topologies can vary substantially even within a given viral group. Five examples with hepatitis B virus and poliovirus are presented to illustrate how covariance network analysis can lead to inferences about viral biology. PMID:22238298

Alternative Multiple Imputation Inference for Mean and Covariance Structure Modeling

ERIC Educational Resources Information Center

Lee, Taehun; Cai, Li

2012-01-01

Model-based multiple imputation has become an indispensable method in the educational and behavioral sciences. Mean and covariance structure models are often fitted to multiply imputed data sets. However, the presence of multiple random imputations complicates model fit testing, which is an important aspect of mean and covariance structure…

A parametric interpretation of Bayesian Nonparametric Inference from Gene Genealogies: Linking ecological, population genetics and evolutionary processes.

PubMed

Ponciano, José Miguel

2017-11-22

Using a nonparametric Bayesian approach Palacios and Minin (2013) dramatically improved the accuracy, precision of Bayesian inference of population size trajectories from gene genealogies. These authors proposed an extension of a Gaussian Process (GP) nonparametric inferential method for the intensity function of non-homogeneous Poisson processes. They found that not only the statistical properties of the estimators were improved with their method, but also, that key aspects of the demographic histories were recovered. The authors' work represents the first Bayesian nonparametric solution to this inferential problem because they specify a convenient prior belief without a particular functional form on the population trajectory. Their approach works so well and provides such a profound understanding of the biological process, that the question arises as to how truly "biology-free" their approach really is. Using well-known concepts of stochastic population dynamics, here I demonstrate that in fact, Palacios and Minin's GP model can be cast as a parametric population growth model with density dependence and environmental stochasticity. Making this link between population genetics and stochastic population dynamics modeling provides novel insights into eliciting biologically meaningful priors for the trajectory of the effective population size. The results presented here also bring novel understanding of GP as models for the evolution of a trait. Thus, the ecological principles foundation of Palacios and Minin (2013)'s prior adds to the conceptual and scientific value of these authors' inferential approach. I conclude this note by listing a series of insights brought about by this connection with Ecology. Copyright © 2017 The Author. Published by Elsevier Inc. All rights reserved.

Analysis of capture-recapture models with individual covariates using data augmentation

USGS Publications Warehouse

Royle, J. Andrew

2009-01-01

I consider the analysis of capture-recapture models with individual covariates that influence detection probability. Bayesian analysis of the joint likelihood is carried out using a flexible data augmentation scheme that facilitates analysis by Markov chain Monte Carlo methods, and a simple and straightforward implementation in freely available software. This approach is applied to a study of meadow voles (Microtus pennsylvanicus) in which auxiliary data on a continuous covariate (body mass) are recorded, and it is thought that detection probability is related to body mass. In a second example, the model is applied to an aerial waterfowl survey in which a double-observer protocol is used. The fundamental unit of observation is the cluster of individual birds, and the size of the cluster (a discrete covariate) is used as a covariate on detection probability.

Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure.

PubMed

Yung, Yiu-Fai; Browne, Michael W; Zhang, Wei

2015-02-01

This paper demonstrates the usefulness and flexibility of the general structural equation modelling (SEM) approach to fitting direct covariance patterns or structures (as opposed to fitting implied covariance structures from functional relationships among variables). In particular, the MSTRUCT modelling language (or syntax) of the CALIS procedure (SAS/STAT version 9.22 or later: SAS Institute, 2010) is used to illustrate the SEM approach. The MSTRUCT modelling language supports a direct covariance pattern specification of each covariance element. It also supports the input of additional independent and dependent parameters. Model tests, fit statistics, estimates, and their standard errors are then produced under the general SEM framework. By using numerical and computational examples, the following tests of basic covariance patterns are illustrated: sphericity, compound symmetry, and multiple-group covariance patterns. Specification and testing of two complex correlation structures, the circumplex pattern and the composite direct product models with or without composite errors and scales, are also illustrated by the MSTRUCT syntax. It is concluded that the SEM approach offers a general and flexible modelling of direct covariance and correlation patterns. In conjunction with the use of SAS macros, the MSTRUCT syntax provides an easy-to-use interface for specifying and fitting complex covariance and correlation structures, even when the number of variables or parameters becomes large. © 2014 The British Psychological Society.

Inter-provider comparison of patient-reported outcomes: developing an adjustment to account for differences in patient case mix.

PubMed

Nuttall, David; Parkin, David; Devlin, Nancy

2015-01-01

This paper describes the development of a methodology for the case-mix adjustment of patient-reported outcome measures (PROMs) data permitting the comparison of outcomes between providers on a like-for-like basis. Statistical models that take account of provider-specific effects form the basis of the proposed case-mix adjustment methodology. Indirect standardisation provides a transparent means of case mix adjusting the PROMs data, which are updated on a monthly basis. Recently published PROMs data for patients undergoing unilateral knee replacement are used to estimate empirical models and to demonstrate the application of the proposed case-mix adjustment methodology in practice. The results are illustrative and are used to highlight a number of theoretical and empirical issues that warrant further exploration. For example, because of differences between PROMs instruments, case-mix adjustment methodologies may require instrument-specific approaches. A number of key assumptions are made in estimating the empirical models, which could be open to challenge. The covariates of post-operative health status could be expanded, and alternative econometric methods could be employed. © 2013 Crown copyright.

Covariant Structure of Models of Geophysical Fluid Motion

NASA Astrophysics Data System (ADS)

Dubos, Thomas

2018-01-01

Geophysical models approximate classical fluid motion in rotating frames. Even accurate approximations can have profound consequences, such as the loss of inertial frames. If geophysical fluid dynamics are not strictly equivalent to Newtonian hydrodynamics observed in a rotating frame, what kind of dynamics are they? We aim to clarify fundamental similarities and differences between relativistic, Newtonian, and geophysical hydrodynamics, using variational and covariant formulations as tools to shed the necessary light. A space-time variational principle for the motion of a perfect fluid is introduced. The geophysical action is interpreted as a synchronous limit of the relativistic action. The relativistic Levi-Civita connection also has a finite synchronous limit, which provides a connection with which to endow geophysical space-time, generalizing Cartan (1923). A covariant mass-momentum budget is obtained using covariance of the action and metric-preserving properties of the connection. Ultimately, geophysical models are found to differ from the standard compressible Euler model only by a specific choice of a metric-Coriolis-geopotential tensor akin to the relativistic space-time metric. Once this choice is made, the same covariant mass-momentum budget applies to Newtonian and all geophysical hydrodynamics, including those models lacking an inertial frame. Hence, it is argued that this mass-momentum budget provides an appropriate, common fundamental principle of dynamics. The postulate that Euclidean, inertial frames exist can then be regarded as part of the Newtonian theory of gravitation, which some models of geophysical hydrodynamics slightly violate.

Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications

PubMed Central

Chaibub Neto, Elias

2015-01-01

In this paper we propose a vectorized implementation of the non-parametric bootstrap for statistics based on sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of sample moment statistics by simply weighting the observed data according to multinomial counts instead of evaluating the statistic on a resampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights and compute the entire vector of bootstrap replications with a few matrix multiplications. Vectorization is particularly important for matrix-oriented programming languages such as R, where matrix/vector calculations tend to be faster than scalar operations implemented in a loop. We illustrate the application of the vectorized implementation in real and simulated data sets, when bootstrapping Pearson’s sample correlation coefficient, and compared its performance against two state-of-the-art R implementations of the non-parametric bootstrap, as well as a straightforward one based on a for loop. Our investigations spanned varying sample sizes and number of bootstrap replications. The vectorized bootstrap compared favorably against the state-of-the-art implementations in all cases tested, and was remarkably/considerably faster for small/moderate sample sizes. The same results were observed in the comparison with the straightforward implementation, except for large sample sizes, where the vectorized bootstrap was slightly slower than the straightforward implementation due to increased time expenditures in the generation of weight matrices via multinomial sampling. PMID:26125965

Parametric and non-parametric species delimitation methods result in the recognition of two new Neotropical woody bamboo species.

PubMed

Ruiz-Sanchez, Eduardo

2015-12-01

The Neotropical woody bamboo genus Otatea is one of five genera in the subtribe Guaduinae. Of the eight described Otatea species, seven are endemic to Mexico and one is also distributed in Central and South America. Otatea acuminata has the widest geographical distribution of the eight species, and two of its recently collected populations do not match the known species morphologically. Parametric and non-parametric methods were used to delimit the species in Otatea using five chloroplast markers, one nuclear marker, and morphological characters. The parametric coalescent method and the non-parametric analysis supported the recognition of two distinct evolutionary lineages. Molecular clock estimates were used to estimate divergence times in Otatea. The results for divergence time in Otatea estimated the origin of the speciation events from the Late Miocene to Late Pleistocene. The species delimitation analyses (parametric and non-parametric) identified that the two populations of O. acuminata from Chiapas and Hidalgo are from two separate evolutionary lineages and these new species have morphological characters that separate them from O. acuminata s.s. The geological activity of the Trans-Mexican Volcanic Belt and the Isthmus of Tehuantepec may have isolated populations and limited the gene flow between Otatea species, driving speciation. Based on the results found here, I describe Otatea rzedowskiorum and Otatea victoriae as two new species, morphologically different from O. acuminata. Copyright © 2015 Elsevier Inc. All rights reserved.

Estimation from PET data of transient changes in dopamine concentration induced by alcohol: support for a non-parametric signal estimation method

NASA Astrophysics Data System (ADS)

Constantinescu, C. C.; Yoder, K. K.; Kareken, D. A.; Bouman, C. A.; O'Connor, S. J.; Normandin, M. D.; Morris, E. D.

2008-03-01

We previously developed a model-independent technique (non-parametric ntPET) for extracting the transient changes in neurotransmitter concentration from paired (rest & activation) PET studies with a receptor ligand. To provide support for our method, we introduced three hypotheses of validation based on work by Endres and Carson (1998 J. Cereb. Blood Flow Metab. 18 1196-210) and Yoder et al (2004 J. Nucl. Med. 45 903-11), and tested them on experimental data. All three hypotheses describe relationships between the estimated free (synaptic) dopamine curves (FDA(t)) and the change in binding potential (ΔBP). The veracity of the FDA(t) curves recovered by nonparametric ntPET is supported when the data adhere to the following hypothesized behaviors: (1) ΔBP should decline with increasing DA peak time, (2) ΔBP should increase as the strength of the temporal correlation between FDA(t) and the free raclopride (FRAC(t)) curve increases, (3) ΔBP should decline linearly with the effective weighted availability of the receptor sites. We analyzed regional brain data from 8 healthy subjects who received two [11C]raclopride scans: one at rest, and one during which unanticipated IV alcohol was administered to stimulate dopamine release. For several striatal regions, nonparametric ntPET was applied to recover FDA(t), and binding potential values were determined. Kendall rank-correlation analysis confirmed that the FDA(t) data followed the expected trends for all three validation hypotheses. Our findings lend credence to our model-independent estimates of FDA(t). Application of nonparametric ntPET may yield important insights into how alterations in timing of dopaminergic neurotransmission are involved in the pathologies of addiction and other psychiatric disorders.

The Probability of Exceedance as a Nonparametric Person-Fit Statistic for Tests of Moderate Length

ERIC Educational Resources Information Center

Tendeiro, Jorge N.; Meijer, Rob R.

2013-01-01

To classify an item score pattern as not fitting a nonparametric item response theory (NIRT) model, the probability of exceedance (PE) of an observed response vector x can be determined as the sum of the probabilities of all response vectors that are, at most, as likely as x, conditional on the test's total score. Vector x is to be considered…

Analyzing Single-Molecule Time Series via Nonparametric Bayesian Inference

PubMed Central

Hines, Keegan E.; Bankston, John R.; Aldrich, Richard W.

2015-01-01

The ability to measure the properties of proteins at the single-molecule level offers an unparalleled glimpse into biological systems at the molecular scale. The interpretation of single-molecule time series has often been rooted in statistical mechanics and the theory of Markov processes. While existing analysis methods have been useful, they are not without significant limitations including problems of model selection and parameter nonidentifiability. To address these challenges, we introduce the use of nonparametric Bayesian inference for the analysis of single-molecule time series. These methods provide a flexible way to extract structure from data instead of assuming models beforehand. We demonstrate these methods with applications to several diverse settings in single-molecule biophysics. This approach provides a well-constrained and rigorously grounded method for determining the number of biophysical states underlying single-molecule data. PMID:25650922

Penalized nonparametric scalar-on-function regression via principal coordinates

PubMed Central

Reiss, Philip T.; Miller, David L.; Wu, Pei-Shien; Hua, Wen-Yu

2016-01-01

A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. PMID:29217963

Nonparametric estimation of benchmark doses in environmental risk assessment

PubMed Central

Piegorsch, Walter W.; Xiong, Hui; Bhattacharya, Rabi N.; Lin, Lizhen

2013-01-01

Summary An important statistical objective in environmental risk analysis is estimation of minimum exposure levels, called benchmark doses (BMDs), that induce a pre-specified benchmark response in a dose-response experiment. In such settings, representations of the risk are traditionally based on a parametric dose-response model. It is a well-known concern, however, that if the chosen parametric form is misspecified, inaccurate and possibly unsafe low-dose inferences can result. We apply a nonparametric approach for calculating benchmark doses, based on an isotonic regression method for dose-response estimation with quantal-response data (Bhattacharya and Kong, 2007). We determine the large-sample properties of the estimator, develop bootstrap-based confidence limits on the BMDs, and explore the confidence limits’ small-sample properties via a short simulation study. An example from cancer risk assessment illustrates the calculations. PMID:23914133

Relativistic covariance of Ohm's law

NASA Astrophysics Data System (ADS)

Starke, R.; Schober, G. A. H.

2016-04-01

The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor χμ ν relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohm's law, we prove the validity of Ohm's law in every inertial frame. We further use the universal relation between χμ ν and the microscopic conductivity tensor σkℓ to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohm's law.

Covariance expressions for eigenvalue and eigenvector problems

NASA Astrophysics Data System (ADS)

Liounis, Andrew J.

There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

Locally-Based Kernal PLS Smoothing to Non-Parametric Regression Curve Fitting

NASA Technical Reports Server (NTRS)

Rosipal, Roman; Trejo, Leonard J.; Wheeler, Kevin; Korsmeyer, David (Technical Monitor)

2002-01-01

We present a novel smoothing approach to non-parametric regression curve fitting. This is based on kernel partial least squares (PLS) regression in reproducing kernel Hilbert space. It is our concern to apply the methodology for smoothing experimental data where some level of knowledge about the approximate shape, local inhomogeneities or points where the desired function changes its curvature is known a priori or can be derived based on the observed noisy data. We propose locally-based kernel PLS regression that extends the previous kernel PLS methodology by incorporating this knowledge. We compare our approach with existing smoothing splines, hybrid adaptive splines and wavelet shrinkage techniques on two generated data sets.

NONPARAMETRIC MANOVA APPROACHES FOR NON-NORMAL MULTIVARIATE OUTCOMES WITH MISSING VALUES

PubMed Central

He, Fanyin; Mazumdar, Sati; Tang, Gong; Bhatia, Triptish; Anderson, Stewart J.; Dew, Mary Amanda; Krafty, Robert; Nimgaonkar, Vishwajit; Deshpande, Smita; Hall, Martica; Reynolds, Charles F.

2017-01-01

Between-group comparisons often entail many correlated response variables. The multivariate linear model, with its assumption of multivariate normality, is the accepted standard tool for these tests. When this assumption is violated, the nonparametric multivariate Kruskal-Wallis (MKW) test is frequently used. However, this test requires complete cases with no missing values in response variables. Deletion of cases with missing values likely leads to inefficient statistical inference. Here we extend the MKW test to retain information from partially-observed cases. Results of simulated studies and analysis of real data show that the proposed method provides adequate coverage and superior power to complete-case analyses. PMID:29416225

Covariation assessment for neutral and emotional verbal stimuli in paranoid delusions.

PubMed

Díez-Alegría, Cristina; Vázquez, Carmelo; Hernández-Lloreda, María J

2008-11-01

Selective processing of emotion-relevant information is considered a central feature in various types of psychopathology, yet the mechanisms underlying these biases are not well understood. One of the first steps in processing information is to gather data to judge the covariation or association of events. The aim of this study was to explore whether patients with persecutory delusions would show a covariation bias when processing stimuli related to social threat. We assessed estimations of covariation in-patients with current persecutory (CP) beliefs (N=40), patients with past persecutory (PP) beliefs (N=25), and a non-clinical control (NC) group (N=36). Covariation estimations were assessed under three different experimental conditions. The first two conditions focused on neutral behaviours (Condition 1) and psychological traits (Condition 2) for two distant cultural groups, while the third condition included self-relevant material by exposing the participant to either protective social (positive) or threatening social (negative) statements about the participant or a third person. Our results showed that all participants were precise in their covariation estimations. However, when judging covariation for self-relevant sentences related to social statements (Condition 3), all groups showed a significant tendency to associate positive social interaction (protection themed) sentences to the self. Yet, when using sentences related to social-threat, the CP group showed a bias consisting of overestimating the number of self-referent sentences. Our results showed that there was no specific covariation assessment bias related to paranoid beliefs. Both NCs and participants with persecutory beliefs showed a similar pattern of results when processing neutral or social threat-related sentences. The implications for understanding of the role of self-referent information processing biases in delusion formation are discussed.

Generating survival times to simulate Cox proportional hazards models with time-varying covariates.

PubMed

Austin, Peter C

2012-12-20

Simulations and Monte Carlo methods serve an important role in modern statistical research. They allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible. A key element in any statistical simulation is the existence of an appropriate data-generating process: one must be able to simulate data from a specified statistical model. We describe data-generating processes for the Cox proportional hazards model with time-varying covariates when event times follow an exponential, Weibull, or Gompertz distribution. We consider three types of time-varying covariates: first, a dichotomous time-varying covariate that can change at most once from untreated to treated (e.g., organ transplant); second, a continuous time-varying covariate such as cumulative exposure at a constant dose to radiation or to a pharmaceutical agent used for a chronic condition; third, a dichotomous time-varying covariate with a subject being able to move repeatedly between treatment states (e.g., current compliance or use of a medication). In each setting, we derive closed-form expressions that allow one to simulate survival times so that survival times are related to a vector of fixed or time-invariant covariates and to a single time-varying covariate. We illustrate the utility of our closed-form expressions for simulating event times by using Monte Carlo simulations to estimate the statistical power to detect as statistically significant the effect of different types of binary time-varying covariates. This is compared with the statistical power to detect as statistically significant a binary time-invariant covariate. Copyright © 2012 John Wiley & Sons, Ltd.

Nonparametric Methods in Astronomy: Think, Regress, Observe—Pick Any Three

NASA Astrophysics Data System (ADS)

Steinhardt, Charles L.; Jermyn, Adam S.

2018-02-01

Telescopes are much more expensive than astronomers, so it is essential to minimize required sample sizes by using the most data-efficient statistical methods possible. However, the most commonly used model-independent techniques for finding the relationship between two variables in astronomy are flawed. In the worst case they can lead without warning to subtly yet catastrophically wrong results, and even in the best case they require more data than necessary. Unfortunately, there is no single best technique for nonparametric regression. Instead, we provide a guide for how astronomers can choose the best method for their specific problem and provide a python library with both wrappers for the most useful existing algorithms and implementations of two new algorithms developed here.

Alternative Payment Models Should Risk-Adjust for Conversion Total Hip Arthroplasty: A Propensity Score-Matched Study.

PubMed

McLawhorn, Alexander S; Schairer, William W; Schwarzkopf, Ran; Halsey, David A; Iorio, Richard; Padgett, Douglas E

2017-12-06

For Medicare beneficiaries, hospital reimbursement for nonrevision hip arthroplasty is anchored to either diagnosis-related group code 469 or 470. Under alternative payment models, reimbursement for care episodes is not further risk-adjusted. This study's purpose was to compare outcomes of primary total hip arthroplasty (THA) vs conversion THA to explore the rationale for risk adjustment for conversion procedures. All primary and conversion THAs from 2007 to 2014, excluding acute hip fractures and cancer patients, were identified in the National Surgical Quality Improvement Program database. Conversion and primary THA patients were matched 1:1 using propensity scores, based on preoperative covariates. Multivariable logistic regressions evaluated associations between conversion THA and 30-day outcomes. A total of 2018 conversions were matched to 2018 primaries. There were no differences in preoperative covariates. Conversions had longer operative times (148 vs 95 minutes, P < .001), more transfusions (37% vs 17%, P < .001), and longer length of stay (4.4 vs 3.1 days, P < .001). Conversion THA had increased odds of complications (odds ratio [OR] 1.75; 95% confidence interval [CI] 1.37-2.24), deep infection (OR 4.21; 95% CI 1.72-10.28), discharge to inpatient care (OR 1.52; 95% CI 1.34-1.72), and death (OR 2.39; 95% CI 1.04-5.47). Readmission odds were similar. Compared with primary THA, conversion THA is associated with more complications, longer length of stay, and increased discharge to continued inpatient care, implying greater resource utilization for conversion patients. As reimbursement models shift toward bundled payment paradigms, conversion THA appears to be a procedure for which risk adjustment is appropriate. Copyright © 2017 Elsevier Inc. All rights reserved.

Evaluation of model-based versus non-parametric monaural noise-reduction approaches for hearing aids.