IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate th...

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Bibliographic Details
Published inActa mathematica scientia Vol. 30; no. 4; pp. 1115 - 1124
Main Author 叶仁道 王松桂
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2010
College of Economics,Hangzhou Dianzi University,Zhejiang 310018,China
College of Applied Sciences,Beijing University of Technology,Beijing 100124,China%College of Applied Sciences,Beijing University of Technology,Beijing 100124,China
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ISSN0252-9602
1572-9087
DOI10.1016/S0252-9602(10)60109-9

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Summary:In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.
Bibliography:O212.1
Covariance matrix; shrinkage estimator; linear mixed model; eigenvalue
O151.21
42-1227/O
Covariance matrix
shrinkage estimator
linear mixed model
eigenvalue
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(10)60109-9