方差分量模型中回归系数的线性估计的可容许性

考虑方差分量模型$ep Y=Xbeta,;cov(Y)=tsm_{i=1}^{m}theta_iV_i$, 其中$ntimes p$矩阵$X$和非负定矩阵$V_i;(i=1,2,cdots,m)$都是已知的, $betain R^p,;theta_igeq 0$或$theta_i>0;(i=1,2,cdots,m)$均为参数bd 在本文中, 我们在二次损失下, 当$mu{(X)} subsetmu{(V)}$时, 给出了关于可估函数$Sbeta$的线性估计在线性估计类中可容许性的充要条件

Admissibility of Linear Estimators of Regression Coefficient in a Variance Component Model

Consider the variance component model $ep Y=Xbeta,;cov(Y)=tsm_{i=1}^mtheta_iV_i$, where $X$: $ntimes p$ and $V_igeq0;(i=1,2,cdots,m)$ are known, $betain R^p$, $theta_igeq0$ or $theta_i>0$ $(i=1,2,cdots,m)$ are parameters. In this paper, when $mu(X)subsetmu(V)$, the sufficient and necessary conditions for a linear estimable estimator of $Sbeta$ to be admissible in the class of all linear estimators are given under quadratic loss function.