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Abstract:
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We consider estimation of mean squared prediction error (MSPE) in small area estimation (SAE) when a procedure of model selection is involved prior to the estimation. We discuss the difficulty of achieving both second-order unbiasedness and positivity at the same time, the so-called double-goal, in MSPE estimation, and propose a simple alternative by estimating the logarithm of the MSPE. A unified Monte-Carlo jackknife method, called McJack, is proposed for estimating the log-MSPE. We prove the second-order unbiasedness of McJack, and demonstrate the performance of McJack in assessing uncertainty in SAE after model selection through empirical investigations that include simulation studies and real-data analyses.
This work is joint with Jiming Jiang of University of California, Davis, and P. Lahiri of University of Maryland, College Park.
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