Asymptotically optimal nonparametric empirical Bayes via predictive recursion

TL;DR

This paper demonstrates that predictive recursion-based empirical Bayes methods are asymptotically optimal for nonparametric estimation of priors, with applications to baseball batting average prediction.

Contribution

It introduces a general notion of asymptotic optimality for empirical Bayes and shows PR-based procedures satisfy this, with practical application to sports data.

Findings

PR-based empirical Bayes achieves asymptotic optimality.

PR method performs well in baseball batting average prediction.

Captures distribution of latent features effectively.

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 paper 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.