Influence functions and robust Bayes and empirical Bayes small area estimation

• 成果类型: Article
• 署名作者: Ghosh, Malay; Maiti, Tapabrata; Roy, Ananya
• 署名单位: State University System of Florida; University of Florida; Iowa State University; University of Nebraska System; University of Nebraska Lincoln
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asn030
• 发表日期: 2008
• 页码: 573585
• 关键词: limiting risk; linear-model; error

摘要

We introduce new robust small area estimation procedures based on area-level models. We first find influence functions corresponding to each individual area-level observation by measuring the divergence between the posterior density functions of regression coefficients with and without that observation. Next, based on these influence functions, properly standardized, we propose some new robust Bayes and empirical Bayes small area estimators. The mean squared errors and estimated mean squared errors of these estimators are also found. A small simulation study compares the performance of the robust and the regular empirical Bayes estimators. When the model variance is larger than the sample variance, the proposed robust empirical Bayes estimators are superior.