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Empirical Bayes Confidence Intervals for Means of Natural Exponential Family‐Quadratic Variance Function Distributions with Application to Small Area Estimation

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  • MALAY GHOSH
  • TAPABRATA MAITI

Abstract

. The paper develops empirical Bayes (EB) confidence intervals for population means with distributions belonging to the natural exponential family‐quadratic variance function (NEF‐QVF) family when the sample size for a particular population is moderate or large. The basis for such development is to find an interval centred around the posterior mean which meets the target coverage probability asymptotically, and then show that the difference between the coverage probabilities of the Bayes and EB intervals is negligible up to a certain order. The approach taken is Edgeworth expansion so that the sample sizes from the different populations need not be significantly large. The proposed intervals meet the target coverage probabilities asymptotically, and are easy to construct. We illustrate use of these intervals in the context of small area estimation both through real and simulated data. The proposed intervals are different from the bootstrap intervals. The latter can be applied quite generally, but the order of accuracy of these intervals in meeting the desired coverage probability is unknown.

Suggested Citation

  • Malay Ghosh & Tapabrata Maiti, 2008. "Empirical Bayes Confidence Intervals for Means of Natural Exponential Family‐Quadratic Variance Function Distributions with Application to Small Area Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 484-495, September.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:3:p:484-495
    DOI: 10.1111/j.1467-9469.2008.00597.x
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    References listed on IDEAS

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    1. Gauri Sankar Datta & Malay Ghosh & David Daniel Smith & Parthasarathi Lahiri, 2002. "On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 139-152, March.
    2. Malay Ghosh, 2004. "Small-area estimation based on natural exponential family quadratic variance function models and survey weights," Biometrika, Biometrika Trust, vol. 91(1), pages 95-112, March.
    3. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
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    Cited by:

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    2. Tatsuya Kubokawa & Mana Hasukawa & Kunihiko Takahashi, 2012. "On Measuring Uncertainty of Benchmarked Predictors with Application to Disease Risk Estimatee," CIRJE F-Series CIRJE-F-861, CIRJE, Faculty of Economics, University of Tokyo.
    3. Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "On Conditional Mean Squared Errors of Empirical Bayes Estimators in Mixed Models with Application to Small Area Estimation," CIRJE F-Series CIRJE-F-934, CIRJE, Faculty of Economics, University of Tokyo.
    4. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2016. "On conditional prediction errors in mixed models with application to small area estimation," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 18-33.

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