一类多元线性模型的一致最小方差无偏估计

The uniformly minimum variance unbiasedestimation of a class of multivariate linear model

本文讨论一类多元线性模型 :y=(S T′) β+e,E(e) =0 ,e=(ε′(1) ,… ,ε′(n) )′,E(ε(i) ε′(n) ) =Φ 0 ,E(ε(i) ε′(i) ε(i) ε′(i) ) =K,i=1 ,2 ,… ,n.当 y准正态分布时 ,在一定意义下得到Φ的 L S估计Φ1,以及 tr(DΦ1)为 tr(DΦ ) (D=D′)的一致对 (Φ ,k)的最小方差无偏估计 (UMVUE)的若干充要条件 .

The present paper considers a class of multivariate linear model y=(ST′)β+e,E(e)=0,e=(ε (1) ′,...,ε (n) ′)′,E(ε (i) ε′ (i) )=Φ0,E(ε (i) ε′ (i) ε (i) ε′ (i) )=K,(i=1,2,...,n).If y is quasinormal distribution,under certain sense,the author,gets the LS estimation Φ 1 of Φ and several necessary and sufficient conditions that tr(DΦ 1) is the minimum variance unbiased estimation(UMVUE)of tr(DΦ) ,(D=D′) with is uniformly with respect to (Φ,K).