| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 87 === The problem of estimating a multivariate normal mean vector has received much attention. The well-known James-Stein estimator dominates the maximum likelihood estimator, that is the sample mean, when the dimension is greater than three. When the mean vector is assumed to be bounded, it is natural to ask if an analogous Stein's phenomenon exists. However, there is no empirical Bayes estimators being studied under this added boundedness assumption, as far as we know. In this thesis, we propose an empirical Bayes estimator which is based on the Bayes rule with respect to the truncated normal prior and is selected by extended numerical results. It is noted that the proposed empirical Bayes estimator dominates the truncated sample mean, the maximum likelihood estimator, if the region containing the parameter is small; but the domination fails if the region is large.
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