Best Predictive Small Area Estimation

• 成果类型: Article
• 署名作者: Jiang, Jiming; Thuan Nguyen; Rao, J. Sunil
• 署名单位: University of California System; University of California Davis; Oregon Health & Science University; University of Miami
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2011.tm10221
• 发表日期: 2011
• 页码: 732-745
• 关键词: mean squared error

摘要

We derive the best predictive estimator (BPE) of the fixed parameters under two well-known small area models, the Fay-Herriot model and the nested-error regression model. This leads to a new prediction procedure, called observed best prediction (OBP), which is different from the empirical best linear unbiased prediction (EBLUP). We show that BPE is more reasonable than the traditional estimators derived from estimation considerations, such as maximum likelihood (ML) and restricted maximum likelihood (REML), if the main interest is estimation of small area means, which is a mixed-model prediction problem. We use both theoretical derivations and empirical studies to demonstrate that the OBP can significantly outperform EBLUP in terms of the mean squared prediction error (MSPE), if the underlying model is misspecified. On the other hand, when the underlying model is correctly specified, the overall predictive performance of the OBP is very similar to that of the EBLUP if the number of small areas is large. A general theory about OBP, including its exact MSPE comparison with the BLUP in the context of mixed-model prediction, and asymptotic behavior of the BPE, is developed. A real data example is considered. A supplementary appendix is available online.