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Robust Bayesian Pitman closeness

Author

Listed:
  • Jafar Ahmadi

    (Ordered and Spatial Data Center of Excellence, Ferdowsi University of Mashhad)

  • Elham Mirfarah

    (Ferdowsi University of Mashhad
    Kharazmi University)

  • Ahmad Parsian

    (University of Tehran)

Abstract

In this paper, the robust Bayesian methodology has been developed in the sense of Pitman measure of closeness. To do this, the definition of Pitman posterior closeness, introduced by Ghosh and Sen (Commun Stat Theory Methods 20:3659–3678, 1991) and simultaneous closeness are integrated. First, the $$\varGamma $$ Γ -minimax problem is developed in the sense of Pitman’s criterion and the basic results and definitions are provided. Then, several results regarding Pitman $$\varGamma $$ Γ -minimax have been proved. Some examples have been presented to illustrate the application of the findings. Finally, other aspect of robust Bayesian methodology such as: Pitman stable rules and Pitman regret type estimators have been proposed.

Suggested Citation

  • Jafar Ahmadi & Elham Mirfarah & Ahmad Parsian, 2016. "Robust Bayesian Pitman closeness," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 671-691, August.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:6:d:10.1007_s00184-015-0572-6
    DOI: 10.1007/s00184-015-0572-6
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    References listed on IDEAS

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    1. Boratynska, Agata, 1997. "Stability of Bayesian inference in exponential families," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 173-178, December.
    2. Fountain, Robert L. & Keating, Jerome P., 1994. "The Pitman comparison of unbiased linear estimators," Statistics & Probability Letters, Elsevier, vol. 19(2), pages 131-136, January.
    3. Meczarski, Marek & Zielinski, Ryszard, 1991. "Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 329-333, October.
    4. Leila Golparver & Ali Karimnezhad & Ahmad Parsian, 2013. "Optimal rules and robust Bayes estimation of a Gamma scale parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 595-622, July.
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