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Asymptotic Correction of Empirical Bayes Confidence Intervals in Small Area Estimation

Author

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

In the small area estimation, the empirical best linear unbiased predictor (EBLUP) in the linear mixed model is recognized useful because it gives a stable and reliable estimate for a mean of a small area. In practical situations where EBLUP is applied to real data, it is important to evaluate how much EBLUP is reliable. One method for the purpose is to construct a confidence interval based on EBLUP. In this paper, we obtain an asymptotically corrected empirical Bayes confidence interval in a nested error regression model with unbalanced sample sizes and unknown components of variance. The coverage probability is shown to satisfy the confidence level in the second order asymptotics. It is numerically revealed that the corrected confidence interval is superior to the conventional confidence interval based on the sample mean in terms of the coverage probability and the expected width of the interval. Finally, it is applied to the posted land price data in Tokyo and the neighboring prefecture.

Suggested Citation

  • Tatsuya Kubokawa, 2007. "Asymptotic Correction of Empirical Bayes Confidence Intervals in Small Area Estimation," CIRJE F-Series CIRJE-F-533, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2007cf533
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