奇异线性模型基于变换观测值的最佳线性无偏估计

The BLUE in the General Gauss-Markoff Model with Linear Transformations of the Observable Variables

摘要: 对于奇异线性回归模型Y =Xβ+ε,ε~（0, ∑）,其中∑≥0,X的秩任意,本文一般地考察观测值的线性变换\tildeY = FY对于系数β的最佳线性无偏估计(BLUE)的影响,得到了由变换带来的参数估计变化的一般结果,文献1关于线性变换保持BLUE最优性的主要结果成为该结果的一个推论,本文还证明了这种变换模型的参数估计问题等价于一个广义均值漂移模型的参数估计问题。

Abstract: Under an arbitrary rank general Gauss-Markoff model Y =Xβ+ε,ε~（0, ∑）, where∑ is a nennegative definite matrix, the effect of transforming the observable variable vector \tildeY = FY is investigated and the general results of difference of the best linear unbiased estimators （BLUE） of C’β due to the transformations are obtained. The result of linear transformations preserving BLUE in the general Gauss-Markoff model is get as a corollary in this paper. It is shown that the effect of the transformations may be analyzed through an associated regression problem which is amenable to solution by two-step least squares.