Empirical Bayes Estimation via the Smoothing by Roughening Approach

Abstract

In many statistical applications, data can be modeled by a compound process where parameters are sampled from a prior (mixing) distribution and data are sampled conditional on parameters. Bayes and empirical Bayes methods are powerful and credible in making inferences from such data, but can be nonrobust. To improve robustness we propose an empirical Bayes approach that replaces a parametric prior by a smoothed non-parametric estimate. The estimation procedure, called smoothing by roughening (SBR), produces robust and efficient estimates and inferences by blending the advantages of both parametric and nonparametric approaches. This article presents large-sample analysis of the SBR approach and proposes a discrete computing algorithm to overcome computational difficulties. We apply the approach to batting average data and toxoplasmosis prevalence data and present results from a series of Monte Carlo simulations evaluating its performance.

Key Words:

• Empirical Bayes
• Discrete computing algorithm
• Hierarchical model
• Nonparametric maximum likelihood estimate