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Empirical Bayes estimation of heteroscedastic variances

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Bibliographic Details
Title: Empirical Bayes estimation of heteroscedastic variances
Authors: Shao, Jun
Publisher Information: Academia Sinica, Institute of Statistical Science, Taipei
Subject Terms: Linear regression, mixed models, consistency, simulation results, error variances, Analysis of variance and covariance (ANOVA), asymptotic unbiasedness, second order expansion of the MSE, robustness, heteroscedastic linear model, data resampling, empirical Bayes estimators, within- group sample variance, variance estimators, Empirical decision procedures, empirical Bayes procedures, weighted least squares, invariance, mean squared error, projection matrix, MINQUE
Description: Summary: Based on data resampling techniques, two classes of empirical Bayes estimators are proposed for estimating the error variances in a heteroscedastic linear model. We concentrate primarily on the situation in which only a few replicates are available at each design point but the total number of observations \(n\) is relatively large. Properties of the empirical Bayes estimators, including invariance, robustness, consistency, asymptotic unbiasedness and mean squared error (MSE), are studied. In particular, a second order expansion of the MSE and an upper bound on the bias of the empirical Bayes estimator are given in terms of the diagonal elements of the projection matrix. Using these results, we compare the empirical Bayes estimator with other existing variance estimators. The MSE of the empirical Bayes estimator is smaller than that of the within-group sample variance and the MINQUE when \(n\) is large. Applications in inferences are also discussed. Some simulation results are presented.
Document Type: Article
File Description: application/xml
Access URL: https://zbmath.org/775917
Accession Number: edsair.c2b0b933574d..996d29d8213e5a53ad87896c7e1a4630
Database: OpenAIRE
Description
Abstract:Summary: Based on data resampling techniques, two classes of empirical Bayes estimators are proposed for estimating the error variances in a heteroscedastic linear model. We concentrate primarily on the situation in which only a few replicates are available at each design point but the total number of observations \(n\) is relatively large. Properties of the empirical Bayes estimators, including invariance, robustness, consistency, asymptotic unbiasedness and mean squared error (MSE), are studied. In particular, a second order expansion of the MSE and an upper bound on the bias of the empirical Bayes estimator are given in terms of the diagonal elements of the projection matrix. Using these results, we compare the empirical Bayes estimator with other existing variance estimators. The MSE of the empirical Bayes estimator is smaller than that of the within-group sample variance and the MINQUE when \(n\) is large. Applications in inferences are also discussed. Some simulation results are presented.