Estimating a Bounded Normal Mean

Let X be a random variable from a normal distribution with unknown mean ? and known variance ?2. In many practical situations, ? is known in advance to lie in an interval, say [?m,m], for some m > 0. As the usual estimator of ?, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of minimax estimation of ? In this paper, by constructing a dominating class of estimators, we show that the maximum likelihood estimator is inadmissible. Then, as a competitor, the Bayes estimator associated with a uniform prior on the interval [?m,m] is proposed. Finally, considering risk performance as a comparison criterion, the estimators are compared and depending on the values taken by ? in the interval [?m,m], the appropriate estimator is suggested.