Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix

Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix

Let S be the matrix of residual sum of square in linear model Y = Aβ + e, where the matrix of errors is distributed as elliptically contoured with unknown scale matrix Σ. For Stein loss function, L1(Σˆ , Σ) = tr(ΣΣˆ −1 )−log |ΣΣˆ −1 |−p, and squared loss function, L2(Σˆ , Σ) = tr(ΣΣˆ −1 −I) 2...

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Main Authors: Z. Khodadadi, B. Tarami
Format: Article
Language:English
Published: Islamic Azad University 2011-06-01
Series:Journal of Mathematical Extension
Online Access:http://ijmex.com/index.php/ijmex/article/view/76
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spelling doaj-09c1672208b549c6a80b624fd4640a642020-11-25T03:36:04ZengIslamic Azad UniversityJournal of Mathematical Extension1735-82991735-82992011-06-01523146Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance MatrixZ. Khodadadi0B. Tarami1Islamic Azad University, Marvdasht-BranchYasouj University, College of SciencesLet S be the matrix of residual sum of square in linear model Y = Aβ + e, where the matrix of errors is distributed as elliptically contoured with unknown scale matrix Σ. For Stein loss function, L1(Σˆ , Σ) = tr(ΣΣˆ −1 )−log |ΣΣˆ −1 |−p, and squared loss function, L2(Σˆ , Σ) = tr(ΣΣˆ −1 −I) 2 , we offer empirical Bayes estimators of Σ, which dominate any scalar multiple of S, i.e., aS, by an effective amount. In fact, this study somehow shows that improvement of the empirical Bayes estimators obtained under the normality assumption remains robust under elliptically contoured modelhttp://ijmex.com/index.php/ijmex/article/view/76
collection DOAJ
language English
format Article
sources DOAJ
author Z. Khodadadi
B. Tarami
spellingShingle Z. Khodadadi
B. Tarami
Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix
Journal of Mathematical Extension
author_facet Z. Khodadadi
B. Tarami
author_sort Z. Khodadadi
title Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix
title_short Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix
title_full Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix
title_fullStr Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix
title_full_unstemmed Robust Empirical Bayes Estimation of the Elliptically Countoured Covariance Matrix
title_sort robust empirical bayes estimation of the elliptically countoured covariance matrix
publisher Islamic Azad University
series Journal of Mathematical Extension
issn 1735-8299
1735-8299
publishDate 2011-06-01
description Let S be the matrix of residual sum of square in linear model Y = Aβ + e, where the matrix of errors is distributed as elliptically contoured with unknown scale matrix Σ. For Stein loss function, L1(Σˆ , Σ) = tr(ΣΣˆ −1 )−log |ΣΣˆ −1 |−p, and squared loss function, L2(Σˆ , Σ) = tr(ΣΣˆ −1 −I) 2 , we offer empirical Bayes estimators of Σ, which dominate any scalar multiple of S, i.e., aS, by an effective amount. In fact, this study somehow shows that improvement of the empirical Bayes estimators obtained under the normality assumption remains robust under elliptically contoured model
url http://ijmex.com/index.php/ijmex/article/view/76
work_keys_str_mv AT zkhodadadi robustempiricalbayesestimationoftheellipticallycountouredcovariancematrix
AT btarami robustempiricalbayesestimationoftheellipticallycountouredcovariancematrix
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