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

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.