Benchmarked empirical Bayes methods in multiplicative area-level models with risk evaluation

• 成果类型: Article
• 署名作者: Ghosh, M.; Kubokawa, T.; Kawakubo, Y.
• 署名单位: State University System of Florida; University of Florida; University of Tokyo; University of Tokyo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv010
• 发表日期: 2015
• 页码: 647659
• 关键词: mean-squared error; estimators; uncertainty

摘要

The paper develops hierarchical empirical Bayes and benchmarked hierarchical empirical Bayes estimators of positive small area means under multiplicative models. The usual benchmarking requirement is that the small area estimates, when aggregated, should equal the direct estimates for the larger geographical areas. However, while estimating positive small area parameters, the conventional squared error or weighted squared error loss subject to the usual benchmark constraint may not produce positive estimators, so it is necessary to seek other loss functions. We consider a multiplicative model for the original data for estimating positive small area means, and suggest a variant of the Kullback-Leibler divergence as a loss function. The prediction errors of the suggested hierarchical empirical Bayes estimators are investigated asymptotically, and their second-order unbiased estimators are provided. Bootstrapped estimators of these prediction errors for both hierarchical empirical Bayes and benchmarked hierarchical empirical Bayes estimators are also given. The performance of the suggested procedures is investigated through simulation as well as with an example.