数学物理学报(英文版) ›› 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

 叶仁道1,2, 王松桂2   

  1. 1. College of Economics, Hangzhou Dianzi University, Zhejiang 310018, China;
    2. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • 收稿日期:2007-03-20 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    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)

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

 YE Ren-Dao1,2, 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)

摘要:

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.

关键词: Covariance matrix, shrinkage estimator, linear mixed model, eigenvalue

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

中图分类号: 

  • 62F03