一般线性混合模型中的最佳线性无偏估计和谱分解估计

The BLUE and Spectral Decomposition Estimator in General Linear Mixed Models

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μ_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.

In this paper, the estimation of a is investigated in general linear mixed models linear combination of fixed and random effects Explicit expression of the best linear unbiased estimator（BLUE） of the combination is derived and it is shown that this BLUE is essentiallyunique where the eovariance 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, μi, and variance components are derived. Furthermore, second-order approximations to the MSE of two-stage estimators based on SDE are obtained.