IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

• Published in: Acta mathematica scientia Vol. 30; no. 4; pp. 1115 - 1124
• Main Author: 叶仁道 王松桂
• Format: Journal Article
• Language: English
• 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
• Subjects: 62F03; 62J07; Covariance matrix; eigenvalue; linear mixed model; shrinkage estimator; 仿真结果; 估计性能; 协方差; 损失函数; 无偏估计; 算术平均; 线性混合模型; Covariance matrix; shrinkage estimator; linear mixed model; 62J07; 62F03; eigenvalue
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(10)60109-9

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.