IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

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

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1115-1124.doi: 10.1016/S0252-9602(10)60109-9

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

叶仁道^1,2, 王松桂²

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-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)

摘要/Abstract

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:

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

中图分类号:

62F03

叶仁道, 王松桂. IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS[J]. 数学物理学报(英文版), 2010, 30(4): 1115-1124.

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.

参考文献

[1] Arnold S F. The Theory of Linear Models and Multivariate Analysis. New York: John Wiley & Sons, 1981

[2] Baltagi B H. Econometric Analysis of Panel Data. Third Edition. New York: John Wiley & Sons, 2005

[3] Dey D K, Srinivasan C. Estimation of a covariance matrix under Stein's loss. Ann Statist, 1985, 13: 1581--1591

[4] Friedman J H. Regularized discriminant analysis. J Amer Statist Assoc, 1989, 84: 165--175

[5] James W, Stein C. Estimation with quadratic loss//Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. vol 1. Berkeley: University of California Press, 1961: 361--379

[6] Leung P L, Chan W Y. Estimation of the scale matrix and its eigenvalues in the Wishart and the multivariate F distributions. Ann Inst Statist Math, 1998, 50: 523--530

[7] Leung P L, Ng F Y. Improved estimation of a covariance matrix in an elliptically contoured matrix distribution. J Multivariate Anal, 2004, 88: 131--137

[8] Muirhead R J. Developments in eigenvalue estimation//Advances in Multivariate Statistical Analysis. Dordrecht: Reidel, 1987: 277--288

[9] Rao C R. Linear Statistical Inferences and its Applications. Second Edition. New York: John Wiley & Sons, 1973

[10] Rao C R, Keleffe J. Estimation of Variance Components and Application. Amsterdam: North-Holland, 1988

[11] Searle S R. Linear Models. New York: John Wiley & Sons, 1971

[12] Searle S R, Casella G, McCulloch C E. Variance Components. New York: John Wiley & Sons, 1992

[13] Shi J H, Wang S G. The generalized spectral decomposition estimates of variance components. Appl Math J Chinese Univ (Ser A), 2005, 20: 83--89

[14] Stein C. Estimation of a covariance matrix (Rietz Lecture). Atlanta: 39th Annual Meeting IMS, 1975

[15] Wang S G, Chow S C. Advanced Linear Model. New York: Marcel Dekker, 1994

[16] Wang S G, Yin S J. A new estimate of the parameters in linear mixed models. Science in China (Ser A), 2002, 45: 1301--1311

[17] Wang S G, Yin S J. Estimating the covariance matrix in linear mixed models by spectral decomposition approach//Proceedings of the Fifth Asian Symposium on Statistics. Beijing: Beijing University of Technology, 2005: 147--156

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	孙美满, 严国政. DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES[J]. 数学物理学报(英文版), 2018, 38(1): 110-124.
[2]	陈化, 陈洪葛, 段忆苪, 胡鑫. LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS[J]. 数学物理学报(英文版), 2017, 37(6): 1653-1664.
[3]	杜锋, 吴传喜, 李光汉, 夏昌玉. UNIVERSAL INEQUALITIES FOR A HORIZONTAL LAPLACIAN VERSION OF THE CLAMPED PLATE PROBLEM ON CARNOT GROUP[J]. 数学物理学报(英文版), 2017, 37(5): 1536-1544.
[4]	贺群, 曾凡奇, 郑大小. ON THE FIRST EIGENVALUE OF THE MEAN FINSLER-LAPLACIAN[J]. 数学物理学报(英文版), 2017, 37(4): 1162-1172.
[5]	G.SOARES. SOME FURTHER NOTES ON THE MATRIX EQUATIONS A^TXB + B^TX^TA = C ANDA^TXB + B^TXA = C[J]. 数学物理学报(英文版), 2015, 35(1): 275-280.
[6]	艾尼·吾甫尔, 艾合买提·卡斯木. FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE[J]. 数学物理学报(英文版), 2014, 34(4): 1301-1330.
[7]	Leszek GASINSKI, Nikolaos S. PAPAGEORGIOU. POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(3): 610-618.
[8]	王江潮, 张贻民. A BIHARMONIC EIGENVALUE PROBLEM AND ITS APPLICATION[J]. 数学物理学报(英文版), 2012, 32(3): 1213-1225.
[9]	Mark Yasuda. SOME PROPERTIES OF COMMUTING AND ANTI-COMMUTING m-INVOLUTIONS[J]. 数学物理学报(英文版), 2012, 32(2): 631-644.
[10]	马冰清. ESTIMATES ON THE FIRST TWO POLY-LAPLACIAN EIGENVALUES ON SPHERICAL DOMAINS[J]. 数学物理学报(英文版), 2012, 32(2): 745-751.
[11]	杨传富, 杨孝平. AMBARZUMYAN’S THEOREM WITH EIGENPARAMETER IN THE BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2011, 31(4): 1561-1568.
[12]	黄广月, 李兴校. ESTIMATES ON EIGENVALUES FOR THE BIHARMONIC OPERATOR ON A BOUNDED DOMAIN IN Hⁿ(−1)[J]. 数学物理学报(英文版), 2011, 31(4): 1383-1388.
[13]	Tedja Santanoe Oepomo. A NEW ALGORITHM FOR COMPUTING LARGEST REAL PART EIGENVALUE OF MATRICES: COLLATZ &\|PERRON-FROBERNIUS&rsquo\|APPROACH[J]. 数学物理学报(英文版), 2011, 31(3): 1189-1202.
[14]	孙和军, 陈大广. ESTIMATES FOR \|EIGENVALUES \|OF FOURTH-ORDER WEIGHTED POLYNOMIAL OPERATOR[J]. 数学物理学报(英文版), 2011, 31(3): 826-834.
[15]	黄广月, 陈文艺. UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER[J]. 数学物理学报(英文版), 2010, 30(3): 939-948.