一类多元线性模型的一致最小方差无偏估计的推广

Extension of the Uniformly Minimum Variance Unbiased Estimation of a Class of Multivariate Linear Model

文 [1 ]讨论一类多元线性模型 : Y=SBT′+ E当 E=Qε,Q=I(单位阵 )且 Cov(ε) =P Φ(随机阵ε准正态分布 ) ,n阶方阵 P≥ 0为已知非零矩阵 .E( ε( i) ε′( i) ) =Φ≥ 0时的一定意义下的情形 .本文讨论线性模型上述式中 Q≠ 0为任意已知矩阵 ,且随机阵 ε只满足某些较弱条件的更一般多元线性模型 .得到包含 [1 ]的 tr( DΦ1)为 tr( DΦ ) ( D=D′)一致对 (Φ ,k)的最小方差无偏估计 ( UMVUE)的若干更一般的充要条件 .

In the author discussed a class of linear model Y=SBT′+E in whichE=Qε,Q=I(the identity matrix) and Cov(ε)=PΦ.Whereε is a random matrix in quasi-mormal distribution;P≥0 is a givenn×n nonyero matrix andE(ε_ (i) ε′_ (i))=Φ≥0,satisfying certain Conditions.In this paper,the author discusses the multivariate linear model(1) whereQ is an arbitrary matrixQ≠0 and the random matrixε satisfies Some weaker Conditions,several general necessary and sufficient Conditions for tr(DΦ_1) to be the uniform minimum variance unbiased estimation (UMVUE) of tr(DΦ)(D=D′)with respect to (Φ,k)are obtained.these results extend the resutls which have been obtained in .