Robust Empirical Bayes Small Area Estimation with Density Power Divergence

TL;DR

This paper introduces a robust empirical Bayes small area estimator using density power divergence to improve performance under distribution misspecification, supported by theoretical derivations and simulation studies.

Contribution

It proposes a novel robust empirical Bayes estimator based on density power divergence, enhancing small area estimation accuracy under model misspecification.

Findings

The proposed estimator is robust against distributional misspecification.

Theoretical derivations of mean squared error are provided.

Simulation and survey data applications demonstrate improved performance.

Abstract

A two-stage normal hierarchical model called the Fay--Herriot model and the empirical Bayes estimator are widely used to provide indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator might be poor when the assumed normal distribution is misspecified. In this article, we propose a simple modification by using density power divergence and suggest a new robust empirical Bayes small area estimator. The mean squared error and estimated mean squared error of the proposed estimator are derived based on the asymptotic properties of the robust estimator of the model parameters. We investigate the numerical performance of the proposed method through simulations and an application to survey data.