Selecting a Minimax Estimator of a Multivariate Normal Mean

The problem of estimating a p-variate normal mean under arbitrary quadratic loss when p ≥ 3 is considered. Any estimator having uniformly smaller risk than the maximum likelihood estimator δ⁰ will have significantly smaller risk only in a fairly small region of the parameter space. A relatively simple minimax estimator is developed which allows the user to select the region in which significant improvement over δ⁰ is to be achieved. Since the desired region of improvement should probably be chosen to coincide with prior beliefs concerning the whereabouts of the normal mean, the estimator is also analyzed from a Bayesian viewpoint.