不完全椭球约束下多元线性模型线性估计的可容许性

本文研究了多元线性模型当未知参数受不完全椭球约束$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$时线性估计的可容许性问题.具体而言,我们研究了约束$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$中$N$和非中心点$\Theta_1$对线性估计的可容许性的影响.主要结果表明在两个不同的不完全椭球约束条件$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$与$\mbox{tr}(\Theta-\Theta_2)'N(\Theta-\Theta_2)\leq\sigma^2$ 下,当$\Theta_1$和$\Theta_2$满足一定的关系时,可容许的齐次线性估计类是相同的.

Admissibility of Linear Estimators in Multivariate\\Linear Models with Respect to an Incomplete\\Ellipsoidal Restriction

This paper studies the admissibility oflinear estimators in multivariate linear models with respect to anincomplete ellipsoidal restriction$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$.Specifically, we study the influence of the matrix $N$ and$\Theta_1$ which is the center of a restricted set to theadmissibility of linear estimators in multivariate linear modelswith respect to the incomplete ellipsoidal restriction$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$. Themain results show that the class of admissible linear estimatorswith the restriction$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$ is thesame as the one with the restriction$\mbox{tr}(\Theta-\Theta_2)'N(\Theta-\Theta_2)\leq\sigma^2$ for$\Theta_1$ and $\Theta_2$ with certain relationship.