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 m less than or equal to rootp. Further descriptions of the cutoff points of small enough radiuses (i.e., m less than or equal to m(0)(p)) for delta(BU) to be minimax are given. These include lower bounds and the large dimension p limiting behaviour of m(0)(p)/rootp. Finally, implications for the associated minimax risk are described. (C) 2002 Elsevier Science B.V. All rights reserved.