College of Statistics and Mathematics, Zhejiang Gongshang University

This paper studies the admissibility of
linear estimators in multivariate linear models with respect to an
incomplete 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 the
admissibility of linear estimators in multivariate linear models
with respect to the incomplete ellipsoidal restriction
$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$. The
main results show that the class of admissible linear estimators
with the restriction
$\mbox{tr}(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2$ is the
same 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.