摘要
对于相依线性回归方程组Ｙｉ＝Ｘｉβｉ＋εｉ（ｉ＝１，２），我们提出了系数向量βｉ的一种较为简便的“朴实”两步估计量，例如β１的估计量为β１（Ｔ）＝（Ｘ′１Ｘ１）－１Ｘ′１Ｙ１－＾σ１２＾σ２２（Ｘ′１Ｘ１）－１Ｘ′１ＴＹ２，其中∑＾＝（σｉｊ）是∑＝（σｉｊ）的一种估计量，本文给出了∑＾的一种新取法，通过均方误差矩阵的大小比较。
In this article, we consider a system of two “Seemingly unrelated regression” equations (Y i=X iβ i+ε i,i=1,2) and examine some finite sample properties of a “naive” two-step estimator of β i given by 1(T)=(X′ 1 X) -1 X′ 1 Y 1- 12 / 22 (X′ 1 X 1) -1 X′ 1 TY 2 ,Where ∑^=( ij ) is an estimator of ∑ =(σ ij ),in particular ∑^=S , the unrestricted estimator. Comparing the mean square error matrix (MSEM) we show that (T) may perform better than the OLS—estimator b 1=(X′ 1 X 1) -1 X′ 1 Y 1 in finite samples We derive necessary and sufficient conditios for MSEM-dominance and outline some testing
