Empirical Bayesball Remixed: Empirical Bayes Methods for Longitudinal Data

• Activity Number: 156
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Roger Koenker*
• Companies: University of Illinois

Abstract

Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A recent convex optimization reformulation of the nonparametric maximum likelihood estimator of Kiefer and Wolfowitz (1956) is employed to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with an application to predicting baseball batting averages, and the age profile of batting performance. An important aspect of the empirical application is the general bivariate specification of the distribution of heterogeneous location and scale effects for players that exhibits a weak positive association between location and scale attributes. Prediction of players' batting averages for 2012 based on performance in the prior decade using the proposed methods shows substantially improved performance over more naive methods with more restrictive treatment of unobserved heterogeneity. Comparisons are also made with nonparametric Bayesian methods based on Dirichlet process priors.