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Small Area Predictors with Dual Shrinkage of Means and Variances

Author

Listed:
  • Hiromasa Tamae

    (Graduate School of Economics, The University of Tokyo)

  • Tatsuya Kubokawa

    (Faculty of Economics, The University of Tokyo)

Abstract

The paper concerns small-area estimation in the Fay-Herriot type area-level model with random dispersions, which models the case that the sampling errors change from area to area. The resulting Bayes estimator shrinks both means and variances, but needs numerical computation to provide the estimates. In this paper, an approximated empirical Bayes (AEB) estimator with a closed form is suggested. The model parameters are estimated via the moment method, and the mean squared error of the AEB is estimated via the single parametric bootstrap method. The benchmarked estimator and a second-order unbiased estimator of the mean squared error are also derived. --

Suggested Citation

  • Hiromasa Tamae & Tatsuya Kubokawa, 2015. "Small Area Predictors with Dual Shrinkage of Means and Variances," CIRJE F-Series CIRJE-F-982, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2015cf982
    as

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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2015/2015cf982.pdf
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    References listed on IDEAS

    as
    1. Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2005. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 92(1), pages 183-196, March.
    2. Tapabrata Maiti & Hao Ren & Samiran Sinha, 2014. "Prediction Error of Small Area Predictors Shrinking Both Means and Variances," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 775-790, September.
    3. G. Datta & M. Ghosh & R. Steorts & J. Maples, 2011. "Bayesian benchmarking with applications to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 574-588, November.
    4. Wang, Junyuan & Fuller, Wayne A., 2003. "The Mean Squared Error of Small Area Predictors Constructed With Estimated Area Variances," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 716-723, January.
    Full references (including those not matched with items on IDEAS)

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