Abstract. Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A new convex optimization formulation of the nonparametric (Kiefer-Wolfowitz) maximum likelihood estimator for mixture models is used to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with some simulation examples as well as an application to predicting baseball batting averages. Comparisons with nonparametric Bayesian methods based on Dirichlet process priors are also provided. It is a truth universally acknowledged, that a statistician in possession of a good shrinkage estimator must be desirous of predicting baseball batting averages. Jane (Yogi) Austen 1
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