关于半相依回归方程组的一类两步Minimax估计的优良性

Optimality of a kind of two-stage minimax estimators for seeminaly unrelated regression equations

本文考虑半相依回归方程系统Y_i=X_iβ_i+ε_i,i=1,2,其中Eε_i=0,Gov(ε_i,ε_j)=σ_(ij)I_n,β_i∈R^(pi),∑=(σ_(ij))_(2×2)>0未知。在矩阵损失函数L(β,δ)=(δ-β)(δ-β)'下,我们证明了Zellner的两步估计是不可容许的,本文提出了参数β_i的一类两步Minimax估计,证明了这一类两步Minimax估计较Zellner的两步估计具有更优良的性质。

In this paper we consider two seeminaly unrelated regression equationsYi (i =1,2),where unknown.We prove that the Zellner's two-stage estimators for βi are inadmissible under the matrix loss function L . So we propose a kind of two-Stage minimax estimators for the regression parameter βi and show that our estimators for βi are better than the two-stage estimators.