Monotone Empirical Bayes Estimators Based on More Informative Samples

Abstract An empirical Bayes estimator is constructed for the case of nonidentical components coming from an exponential family of distributions that is closed under convolution. Examples are the normal, Poisson, and binomial distributions. The construction is based on Robbins' approach to empirical Bayes estimation and generalizes results of O'Bryan and Stijnen and Van Houwelingen. The method is elaborated for the normal and Poisson case, and examples are given that show that this approach gives results comparable to those from the nonparametric maximum likelihood approach of Laird.

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