IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

doi:10.1016/S0252-9602(10)60109-9

Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (4): 1115-1124.doi: 10.1016/S0252-9602(10)60109-9

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IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

YE Ren-Dao^1,2, WANG Song-Gui²

Received:2007-03-20 Online:2010-07-20 Published:2010-07-20
Supported by:
This work was supported by the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (0506011200702), National Natural Science Foundation of China, Tian Yuan Special Foundation (10926059), Foundation of Zhejiang Educational Committee (Y200803920), and Scientific Research Foundation of Hangzhou Dianzi University (KYS025608094)

Abstract

Abstract:

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.

Key words: Covariance matrix, shrinkage estimator, linear mixed model, eigenvalue

CLC Number:

62F03

YE Ren-Dao, WANG Song-Gui. IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS[J].Acta mathematica scientia,Series B, 2010, 30(4): 1115-1124.

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IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

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