Admissible Minimax Estimation of a Multivariate Normal Mean with Arbitrary Quadratic Loss

Abstract

The problem of estimating the mean of a $p$-variate $(p \geqq 3)$ normal distribution is considered. It is assumed that the covariance matrix $\not\sum$ is known and that the loss function is quadratic. A class of minimax estimators is given, out of which admissible minimax estimators are developed.