| 一般线性混合模型中的最佳线性无偏估计和谱分解估计 |
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| 引用本文： | 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(A辑),2009,29(2):223-232. |
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| 作者姓名： | 徐礼文 王松桂 |
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| 作者单位： | 徐礼文,XU Liwen(北方工业大学理学院,北京,100144;清华大学数学科学系,北京,100084);王松桂,WANG Songgui(北京工业大学应用数理学院,北京,100022)
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| 基金项目： | 中国博士后科学基金，国家自然科学基金 |
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| 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ui 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.
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| 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 |
| 收稿时间： | 2007-11-05 |
| 修稿时间： | 2008-12-03 |
The BLUE and Spectral Decomposition Estimator in General Linear Mixed Models |
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| XU Li-Wen,WANG Song-Gui.The BLUE and Spectral Decomposition Estimator in General Linear Mixed Models[J].Acta Mathematica Scientia,2009,29(2):223-232. |
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| Authors: | XU Li-Wen WANG Song-Gui |
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| Affiliation: | (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) |
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| 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, ui, and variance components are derived. Furthermore, second-order approximations to the MSE of two-stage estimators based on SDE are obtained. |
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| Keywords: | Linear mixed modelszz Unbalance datazz Best linear unbiased estimatorzz Two-stage estimatorzz Variance componentszz |
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