线性模型中误差方差的非齐次估计的可容许性
THE ADMISSIBILITY OF NON-HOMOGENE OUS ESTIMATE OF VARIANCE IN LINEAR MODEL
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摘要: 考虑模型Y=Xβ+e,其中Xn×p是设计矩阵,e的各分量e1,e2,…,en相互独立,E（ei）=E（ei3）=0,E（ei2）=σ2,E（ei4）=3σ4,i=1,2,…,n。本文讨论误差方差σ2的估计在估计类\mathscrQ=Y′AY+l′AY+f;Y′AY+l′AY+f≥0对一切Y中的可容许性问题。当X为满秩矩阵时,给出了σ2的估计在\mathscrQ中可容许的充分必要条件,当Xn×p=1时,给出了估计类\mathscrQ的一个完全类以及估计可容许的充分条件。Abstract: Consider model Y=Xβ+e, where Xn×p is a design matrix, e1,e2,…,en, iid. withE（ei）=E（ei3）=0,E（ei2）=σ2,E（ei4）=3σ4,i=1,2,…,n. We discussed the problem about admissibility of the estimate of σ2 in the class \mathscrQ=Y'AY+l'AY+f;Y'AY+l'AY+f≥0, for any Y. Here was offered a necessary and sufficient condition of admissibility if rank (Xn×p) =n; and we gave one complete class of \mathscrQ and a sufficient oondition under which the estimator was admissible if Xn×p=I.
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