Observed best prediction via nested-error regression with potentially misspecified mean and variance

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Jiming Jiang, Thuan Nguyen and J. Sunil Rao^Note 1

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Abstract

We consider the observed best prediction (OBP; Jiang, Nguyen and Rao 2011) for small area estimation under the nested-error regression model, where both the mean and variance functions may be misspecified. We show via a simulation study that the OBP may significantly outperform the empirical best linear unbiased prediction (EBLUP) method not just in the overall mean squared prediction error (MSPE) but also in the area-specific MSPE for every one of the small areas. A bootstrap method is proposed for estimating the design-based area-specific MSPE, which is simple and always produces positive MSPE estimates. The performance of the proposed MSPE estimator is evaluated through a simulation study. An application to the Television School and Family Smoking Prevention and Cessation study is considered.

Key Words: Designe-based MSPE; Heteroscedasticity; Model misspecification; OBP; Small area estimation; TVSFP.

Table of content

• 1. Introduction
• 2. Simulation studies: OBP vs EBLUP
• 3. Estimation of area-specific MSPE
• 4. An application
• Acknowledgements
• Appendix
• References

Notes