不完全椭球约束下多元线性模型线性估计的可容许性

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

摘要: 本文研究了多元线性模型当未知参数受不完全椭球约束\mboxtr (\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\mboxtr(\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\mboxtr(\Theta-\Theta_1)' N(\Theta-\Theta_1)\leq\sigma^2与\mboxtr(\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.

Abstract: This paper studies the admissibility of linear estimators in multivariate linear models with respect to an incomplete ellipsoidal restriction \mboxtr(\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 the admissibility of linear estimators in multivariate linear models with respect to the incomplete ellipsoidal restriction \mboxtr(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2. The main results show that the class of admissible linear estimators with the restriction \mboxtr(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2 is the same as the one with the restriction \mboxtr(\Theta-\Theta_2)'N(\Theta-\Theta_2)\leq\sigma^2 for \Theta_1 and \Theta_2 with certain relationship.