Best predictive small area estimation

Jiming Jiang, Thuan Nguyen, J. Sunil Rao

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)732-745
Number of pages14
JournalJournal of the American Statistical Association
Volume106
Issue number494
DOIs
StatePublished - Jun 1 2011

Keywords

  • Fay-herriot model
  • Mean squared prediction error (MSPE)
  • Model misspecification
  • Nested-error regression model
  • Robustness

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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