  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.
