Minimax estimation of a bounded normal mean vector

Abstract

The problem of minimax estimation of a multivariate normal mean vector has received much attention in recent years. In this paper this problem is considered when the mean vector is restricted to a compact convex subset B of R p . The cases of rectangular and spherical bounds are considered. The least favorable prior distributions and Bayes minimax estimator of the mean vector are obtained for the situation where B is a sphere of sufficiently small radius.