On Bootstrap Averaging Empirical Bayes Estimators

TL;DR

This paper introduces a bootstrap averaging (bagging) method to enhance the stability and performance of parametric empirical Bayes estimators, especially in small sample scenarios, demonstrated through simulations and empirical studies.

Contribution

It proposes a novel bootstrap averaging approach to improve empirical Bayes estimators under small sample conditions, applicable to hierarchical models.

Findings

Bagging improves estimator stability.

Enhanced performance in small sample settings.

Method outperforms classical EB estimators in simulations.

Abstract

Parametric empirical Bayes (EB) estimators have been widely used in variety of fields including small area estimation, disease mapping. Since EB estimator is constructed by plugging in the estimator of parameters in prior distributions, it might perform poorly if the estimator of parameters is unstable. This can happen when the number of samples are small or moderate. This paper suggests bootstrapping averaging approach, known as "bagging" in machine learning literatures, to improve the performances of EB estimators. We consider two typical hierarchical models, two-stage normal hierarchical model and Poisson-gamma model, and compare the proposed method with the classical parametric EB method through simulation and empirical studies.