Minimaxity of empirical bayes estimators of the means of independent normal variables with unequal variances

Abstract

The problem of simultaneous estimation of normal means is considered when variances are unequal and the loss is sum of squared errors. Minimaxity or non-minimaxity of empirical Bayes estimators is investigated when the common prior distribution is given by normal one with mean 0. Minimaxity results for the case when the loss is a weighted sum of squared errors is also given. Monte Carlo simulation results are given to compare the risk behavior of the empirical Bayes estimator with those of other minimax ones.

Keywords:

• Stein estimator
• squared error loss function
• uniform improvement
• weighted sum of squared error loss