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$\ep Y=X\beta,\cov(Y)=\tsm_{i=1}^{m}\theta_iV_i$, 其中$n\times p$矩阵$X$和非负定矩阵$V_i(i=1,2,\cdots,m)$都是已知的, $\beta\in R^p,\theta_i\geq 0$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$\mu{(X)} \subset\mu{(V)}$时, 给出了关于可估函数$S\beta$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 $\ep Y=X\beta,\cov(Y)=\tsm_{i=1}^m\theta_iV_i$, where $X$: $n\times p$ and $V_i\geq0(i=1,2,\cdots,m)$ are known, $\beta\in R^p$, $\theta_i\geq0$ or $\theta_i>0$ $(i=1,2,\cdots,m)$ are parameters. In this paper, when $\mu(X)\subset\mu(V)$, the sufficient and necessary conditions for a linear estimable estimator of $S\beta$ to be admissible in the class of all linear estimators are given under quadratic loss function.