相依回归方程系数的一种估计量的容许性和有效性

ADMISSIBILITY AND EFFICIENCY OF AN ESTIMATOR IN TWO SEEMINGLY UNRELATED REGRESSIONS SYSTEM

对两相依回归方程系统：Ｙ＿ｉ＝Ｘ＿ｉβ＿ｉ＋ε＿ｉ（ｉ＝１，２），Ｅ（ε＿ｉ）＝Ｏ，Ｃｏｖ（εｉ＿，ε＿ｊ）＝σ＿（ｉｊ）Ｉ，刘金山提出了一种可优效于最佳线性无偏估计的新估计．本文结果表明，在线性估计类中β＿ｉ是β＿ｉ的可容许估计；在均方误差准则下，β＿ｉ可优效于协方差改进估计和ＬＳ估计ｂｉ．本文还提出了关于估计占优充要条件的检验统计量和等价假设检验方法．

For the system of two seemingly unrelated regres8iOns:Y_i=X_iβ_i+ε_i(i=1,2)with E(ε_i)=0,Cov(ε_i,ε_j)=σ_(ij)I,Liu Jinshan intreduced a simple estimator of β_i given bywhere is the LS-estimatior. In this paper, the admissibility of within the class of linear estimatiors is proved. Taking the mean square error(MSE) as the standard for comparison, this paper shows that may work better than a com-peting estimator proposed and may perform better than the LS- es-timator bi.And deriv enecesstsary and sufficient-conditions for MSE-dominance and proposesome equivalence test;which are independent of matrix Σ=(σ_(ij)) for the condItions.