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Admissibility and Minimaxity of Benchmarked Shrinkage Estimators

Author

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

  • William E. Strawderman

    (Department of Statistics, Rutgers University)

Abstract

This paper studies decision theoretic properties of benchmarked estimators which are of some importance in small area estimation problems. Benchmarking is intended to improve certain aggregate properties (such as study-wide averages) when model based estimates have been applied to individual small areas. We study admissibility and minimaxity properties of such estimators by reducing the problem to one of studying these problems in a related derived problem. For certain such problems we show that unconstrained solutions in the original (unbenchmarked) problem give unconstrained Bayes, minimax or admissible estimators which automatically satisfy the benchmark constraint. We illustrate the results with several examples. Also, minimaxity of a benchmarked empirical Bayes estimator is shown in the Fay-Herriot model, a frequently used model in small area estimation.

Suggested Citation

  • Tatsuya Kubokawa & William E. Strawderman, 2011. "Admissibility and Minimaxity of Benchmarked Shrinkage Estimators," CIRJE F-Series CIRJE-F-809, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2011cf809
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2011/2011cf809.pdf
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    References listed on IDEAS

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    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. 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.
    3. Kubokawa, Tatsuya & Strawderman, William E., 2007. "On minimaxity and admissibility of hierarchical Bayes estimators," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 829-851, April.
    4. Frey, Jesse & Cressie, Noel, 2003. "Some results on constrained Bayes estimators," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 389-399, December.
    5. Pfeffermann, Danny & Tiller, Richard, 2006. "Small-Area Estimation With StateSpace Models Subject to Benchmark Constraints," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1387-1397, December.
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