On the minimax estimator of a bounded normal mean

For estimating under squared-error loss the mean of a p-variate normal distribution when this mean lies in a ball of radius m centered at the origin and the covariance matrix is equal to the identity matrix, it is shown that the Bayes estimator with respect to a uniformly distributed prior on the boundary of the parameter space ([delta]BU) is minimax whenever . Further descriptions of the cutoff points of small enough radiuses (i.e., m[less-than-or-equals, slant]m0(p)) for [delta]BU to be minimax are given. These include lower bounds and the large dimension p limiting behaviour of . Finally, implications for the associated minimax risk are described.