CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2009, 25(5) 513-518 DOI:      ISSN: 1001-4268 CN: 31-1256

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

Wu Jianhong

College of Statistics and Mathematics, Zhejiang Gongshang University

Abstract��

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.

Keywords�� Admissibility   incomplete ellipsoidal restriction   linear estimators   multivariate linear models.