一般线性混合模型中的最佳线性无偏估计和谱分解估计

Abstract

Abstract:

In this paper, the estimation of a linear combination of fixed and random effects is investigated in general linear mixed models. Explicit expression of the best linear unbiased estimator(BLUE) of the combination is derived and it is shown that this BLUE is essentially-unique where the covariance matrix of the vector of observations may be singular. For the three small-area models that are all special cases of the general linear mixed model, spectral decomposition estimators(SDE) of small area mean, u_i, and variance components are derived. Furthermore, second-order approximations to the MSE of two-stage estimators based on SDE are obtained.

Key words: Linear mixed models, Unbalance data, Best linear unbiased estimator, Two-stage estimator, Variance components

CLC Number:

62J05

XU Li-Wen, WANG Song-Gui. The BLUE and Spectral Decomposition Estimator in General Linear Mixed Models[J].Acta mathematica scientia,Series A, 2009, 29(2): 223-232.

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References

[1] Laird N M, Ware J M. Random effects models for longitudinal data. Biometrics, 1982, 38: 963--974

[2] Robinson G K. That BLUP is a good thing: the estimation of random effects. Statist Sci, 1991, 6: 15--51

[3] Henderson C R. Best linear unbiased estimation and prediction under a selection model. Biometrics, 1975, 31: 423--447

[4] Harville D A. Extension of the Gauss-Markov theorem to include the estimation of random effects. Ann Statist, 1976, 4: 384--395

[5] 陈希孺, 王松桂. 线性模型中的最小二乘法. 上海: 上海科学技术出版社, 2003

[6] Kackar R N, Harville D A. Unbiasedess of two-stage estimation and prediction procedures for mixed linear models. Commun Statist-Theory Meth, 1981, 10: 1249--1261

[7] Kackar R N, Harville D A. Approximations for standard errors of fixed and random effects in mixed linear models. J Amer Statist Assoc, 1984, 79: 853--862

[8] Prasad N G N, Rao J N K. The estimation of mean squared errors of small area estimators. J Amer Statist Assoc, 1990, 85: 163--171

[9] Harville D A, Jeske D R. Mean squared error of estimation or prediction under a general linear model. J Amer Statist Assoc, 1992, 87: 724--731

[10] Datta G S, Lahiri P. A unified measure of uncertainty of estimated best linear unbiased predictors in small
area estimation problems. Statist Sinica, 2000, 10: 613--627

[11] Das K, Jiang J, Rao J N K. Mean squared error of empirical predictor. Ann Statist, 2004, 32: 818--840

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

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

[14] 王松桂等. 线性模型引论. 北京: 科学出版社, 2004

[15] Battese G E, Harter R M, Fuller W A. An error-components model for prediction of county crop areas using
survey and satellite data. J Amer Statist Assoc, 1988, 83: 28--36

[16] Dempster A P, Rubin D B, Tsutakawa R K. Estimation in covariance component models. J Amer Statist Assoc, 1981, 76: 341--353

[17] Fay R E, Herriot R A. Estimates of income for small places: an application of James-Stein procedures to census data. J Amer Statist Assoc, 1979, 74: 269--277

[18] Kubokawa T. Estimation of variance components in mixed linear models. J Multivariate Anal, 1995, 53: 210--236

[19] Rao C R, Kleffe J. Estimation of Variance Components and Applications. New York: North-Holland, 1988

[20] 王松桂, 杨振海. 广义逆矩阵及其应用. 北京: 北京工业大学出版社, 1996

The BLUE and Spectral Decomposition Estimator in General Linear Mixed Models

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