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Stability of Bayesian inference in exponential families

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  • Boratynska, Agata

Abstract

The problem of estimating the unknown parameter of a one-parameter exponential family with the conjugate prior is considered. Some uncertainty about the prior is assumed by introducing a class of priors [Gamma]. The most robust and conditional [Gamma]-minimax estimators are constructed. The situations when those estimators coincide are presented. The paper is a generalization of the result for the Poisson distribution obtained in Mezarski and Zielinski (1991).

Suggested Citation

  • Boratynska, Agata, 1997. "Stability of Bayesian inference in exponential families," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 173-178, December.
    • Handle: RePEc:eee:stapro:v:36:y:1997:i:2:p:173-178
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    References listed on IDEAS

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    1. DasGupta A. & Studden W. J., 1989. "Frequentist Behavior Of Robust Bayes Estimates Of Normal Means," Statistics & Risk Modeling, De Gruyter, vol. 7(4), pages 333-362, April.
    2. Boratyńska Agata & Męczarski Marek, 1994. "Robust Bayesian Estimation In The One-Dimensional Normal Model," Statistics & Risk Modeling, De Gruyter, vol. 12(3), pages 221-230, March.
    3. Eichenauer-Herrmann J., 1991. "Gamma-Minim Ax Estimation In Exponential Families With Quadratic Variance Functions," Statistics & Risk Modeling, De Gruyter, vol. 9(4), pages 319-326, April.
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    Cited by:

    1. 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.
    2. 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.

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