Robust Empirical Bayes Small Area Estimation with Density Power Divergence

2017/02/22 by Shonosuke Sugasawa, Sugasawa, Shonosuke
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.1702.06635

openalex publication_date 2017/02/22 · openalex created_date 2017/03/23 · openalex updated_date 2026/07/28

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.

Citations

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