Robust empirical Bayes small area estimation with density power divergence

• 成果类型: Article
• 署名作者: Sugasawa, S.
• 署名单位: University of Tokyo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz075
• 发表日期: 2020
• 页码: 467480
• 关键词: bootstrap methods; uncertainty; models

摘要

A two-stage normal hierarchical model called the Fay-Herriot model and the empirical Bayes estimator are widely used to obtain indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator can be poor when the assumed normal distribution is misspecified. This article presents a simple modification that makes use of density power divergence and proposes 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.