摘要
对于由两个相依回归方程组成的相依回归系统Ｙｉ＝Ｘｉβｉ＋εｉ（ｉ＝１，２），本文提出了参数βｉ的一种含有待定系数的估计方法。例如，β１的估计为：β＾＊１（Ｋ）＝（Ｘ＇１Ｘ１）－１Ｘ＇１（Ｙ１－σ１２／σ２２Ｎ２Ｙ２－Ｋσ＾２１２／σ１１σ２２Ｐ２Ｙ１），其中Ｋ是待定常数，与β＾＊１（Ｋ）对应的非限定两步估计记为β＾＊１（Ｋ，Ｔ）。当Ｋ＝０时，β＾＊１（Ｋ）等于协方差改进估计＾∧β１（见［１］）。
For the system of two seemingly unrelated regression equations: Yi= Xiβi+8i (i=1, 2), a new method of estimating βi's is introduced in this paper. Theestimator of β1 is given as β1*(K) = (X'1X1)-1X'1Y1-σ12/σ22(X'1X1)-1X1N2Y2-K×(X'1X1)-1X'1P2Y1, where K is an arbitrary constant. The unrestricted two-step estimator, which is the feasible counterpart to β1*(K), is denoted as β1*(K, T). In particular, β*1(0)=β1, the covariance improved estimator introduced in [1], and β1*(1) =β1, a biased estimator introduced in [2]. It is shown that choosing a reasonable K, the estimator β1*(K) may work better than β1, and β1*(K, T) may perform better than ,β1(T), with respect to the mean square error matrix (MSEM) criterion. How to choose the optimal value of K is also discussed.
出处
《应用概率统计》
CSCD
北大核心
1994年第1期78-83,共6页
Chinese Journal of Applied Probability and Statistics
