Asymptotically Optimal Nonparametric Empirical Bayes Via Predictive Recursion

Abstract

An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This article presents a general notion of empirical Bayes asymptotic optimality, and it is shown that PR-based procedures satisfy this property under certain conditions. As an application, the problem of in-season prediction of baseball batting averages is considered. There the PR-based empirical Bayes rule performs well in terms of prediction error and ability to capture the distribution of the latent features.

Keywords:

• Batting average
• Compound decision problem
• Density estimation
• High-dimensional
• Mixture model

Mathematics Subject Classification:

• Primary 62C12, 62G07
• Secondary 62L20