广义协方差改进估计的优良性

Optimality of Generalized Covariance Improvement Estimate

对半相依回归线性系统,我们周期地使用迭加信息的方法,得出了回归系数广义协方差改进估计。这个估计系列的方差是单调不增的。它改进了回归系数的协方差改进估计。特别当m=2时,我们不对误差向量的分布及设计阵之间的关系作出任何假设,而得到广义协方差改进估计的极限便是BLUE的结果;当协方差阵未知时,得到了两步估计的表达式。

In this paper we repeatedly draw information from the seemingly unrelated regression equations and introduce a method that can be used to improve the covariance improvement estimate(CIE). Then the generalized CIE (GCIE) is obtained. When m=2, without any restriction on the rela- tionship between the design matrices or on the distribution of the error vectors,we prove that the limit of GCIE of β_ⅰ(ⅰ=1,2) is BLUE. Moreover,if the covariance matrix is unknown two-stage estimator is obtained.