Improving on the MLE of a bounded normal mean
有界正态均值的极大似然估计改进
We consider the problem of estimating the mean of a $p$-variate normal distribution with identity covariance matrix when the mean lies in a ball of radius $m$. It follows from general theory that dominating estimators of the maximum likelihood estimator always exist when the loss is squared error. We provide and describe explicit classes of improvements for all problems $(m, p)$. We show that,for small enough $m$, a wide class of estimators, including all Bayes estimators…