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Minimaxity of empirical bayes estimators of the means of independent normal variables with unequal variances |
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| Authors: | Nobuo Shinozaki Yuan-Tsung Chang |
| Affiliation: | 1. Faculty of Policy Management , Keio University , Fujisawa, Kanagawa, 252, Japan;2. Department of Management Information , Junior College of Tokiwa University , Miwa, Mito, 310, Japan |
| 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 |