一般线性混合模型中的最佳线性无偏估计和谱分解估计

数学物理学报 ›› 2009, Vol. 29 ›› Issue (2): 223-232.

一般线性混合模型中的最佳线性无偏估计和谱分解估计

徐礼文, 王松桂

(北方工业大学理学院北京 100144|清华大学数学科学系北京 100084)|(北京工业大学应用数理学院北京 100022)

收稿日期:2007-11-05 修回日期:2008-12-03 出版日期:2009-04-25 发布日期:2009-04-25
基金资助:
中国博士后科学基金(20070410544)和国家自然科学基金(10801085)资助

The BLUE and Spectral Decomposition Estimator in General Linear Mixed Models

XU Li-Wen, WANG Song-Gui

(College of Sciences, North China University of Technology, Beijing 100144|Department of Mathematical Sciences, Tsinghua University, |Beijing |100084)|(College of Applied Sciences, |Beijing University of Technology, |Beijing 100022)

Received:2007-11-05 Revised:2008-12-03 Online:2009-04-25 Published:2009-04-25
Supported by:
中国博士后科学基金(20070410544)和国家自然科学基金(10801085)资助

摘要/Abstract

摘要：

该文在一般线性混合模型中, 研究了固定和随机效应线性组合的估计问题. 对观测向量的协方差阵可以为奇异矩阵情形下, 导出了该组合的最佳线性无偏估计,并证明了它的唯一性. 在一般线性混合模型的特例, 三个小域模型下, 得到了小域均值u_i和方差分量的谱分解估计. 进而, 获得了基于谱分解估计的两步估计均方误差的二阶逼近.

关键词: 线性混合模型, 非平衡数据, 最佳线性无偏估计, 两步估计, 方差分量

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

中图分类号:

62J05

徐礼文, 王松桂. 一般线性混合模型中的最佳线性无偏估计和谱分解估计[J]. 数学物理学报, 2009, 29(2): 223-232.

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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