矩阵损失下期望向量的非齐次线性可容许估计

Admissible Nonhomogenous Linear Estimator of Mean Vector Under Matrix Loss

:设Y1 ,Y2 ,… ,Yn 独立同分布 ,EY1 =β ,DY1 =V ,这里 β∈Rm 与V :mxm >0均未知。取矩阵损失函数L(d ,β) =(d - β) (d - β)′ ,估计类￡ =∑ni =1LiYi+b ;Li 为m阶方阵 ,i=1,… ,n ;b∈Rm 。本文在矩阵损失下给出了非齐次线性估计在￡中是

Suppose Y 1,Y 2,…,Yn i.i.d,EY 1=β,DY 1=V,where both β∈R m and V:mxm>0 are unknown. let L(d,β)=(d-β)(d-β)′and ￡=∑ni=1L iY i+b;L i is an mxm real matrix i=1,…,n;b∈R m。In this paper, we give the necessary and sufficient conditions that a nonhomogenous Linear estimator of β is admissible among ￡.