相依回归系统回归系数的待定系数估计

The Undetermined Coefficient Estimate of Regression Coefficients for Seemingly Unrelatede Regression System

对于两个相依线性回归方程组成的系统（１．１），本文提出了β１的待定系数估计β１（ｋ，ｃ）＝（ｘ１１ｘ１＋ｋＩ）－１，其中岭参数ｋ≥０，２是待定系数·与β１（ｋ，ｃ）对应的非限定两步估计记为β１（Ｔ，Ｋ，Ｃ）．当Ｃ＝１时β１（Ｋ，１）＝β１（Ｋ）和β１（Ｔ，Ｋ，１）＝β１（Ｔ，Ｋ）等于［６］引入的一双有偏估计，结果表明总可以选取适当的ｃ值和Ｋ值使β１（Ｋ，ｃ）和β１（Ｔ，Ｋ，ｃ）在均方误差阵准则下分别优于β１和β１（Ｔ）［５］，并讨论了ｃ值的最佳选择问题．

In this paper the undetermined coefficient estimator of gβ1,, β1 (k,c)= (x' 1x1+KI)-1 [x' 1y1 -c. (δ12/δ22,)x'1N2y2] is proposed for the system of two seemingly unrelated regression equations (1. 1), where the ridge parameter k≥0, and c is an arbitrary constant.The unrestricted two-step estimator, where is the feasible counterepart to β1 (k,c),is written as β1 (T,k,c). When c=1, β1 (k,c)=β1 (k) and β1 (T,k,1 )= β1, (T,k),a pair of biasedestimators is introduced in [6]. It is shown that choosing the reasonable c and k values, the estimator β1 (k,c) may work better than β1[5], and β1 (T,k,c) may perform better that β1(T)[5], with respect to the mean square error matrix (MSEM) criterion, and how to choose the optimal value of c is also discussed.