On the estimation of a restricted normal mean,

Let X ~ N([theta],1), where [theta] [epsilon] [-m, m], for some m> 0, and consider the problem of estimating [theta] with quadratic loss. We show that the Bayes estimator [delta]m, corresponding to the uniform prior on [-m, m], dominates [delta]0 (x) = x on [-m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that [delta]m has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981).