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Robust Bayesian prediction and estimation under a squared log error loss function

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  • Kiapour, A.
  • Nematollahi, N.

Abstract

Robust Bayesian analysis is concerned with the problem of making decisions about some future observation or an unknown parameter, when the prior distribution belongs to a class [Gamma] instead of being specified exactly. In this paper, the problem of robust Bayesian prediction and estimation under a squared log error loss function is considered. We find the posterior regret [Gamma]-minimax predictor and estimator in a general class of distributions. Furthermore, we construct the conditional [Gamma]-minimax, most stable and least sensitive prediction and estimation in a gamma model. A prequential analysis is carried out by using a simulation study to compare these predictors.

Suggested Citation

  • Kiapour, A. & Nematollahi, N., 2011. "Robust Bayesian prediction and estimation under a squared log error loss function," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1717-1724, November.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:11:p:1717-1724
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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. 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. Zen Mei-Mei & DasGupta A., 1993. "Estimating A Binomial Parameter: Is Robust Bayes Real Bayes?," Statistics & Risk Modeling, De Gruyter, vol. 11(1), pages 37-60, January.
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    Cited by:

    1. Boratyńska, Agata, 2017. "Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 135-140.
    2. Ali Karimnezhad & Mahmoud Zarepour, 2020. "A general guide in Bayesian and robust Bayesian estimation using Dirichlet processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(3), pages 321-346, April.
    3. 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.
    4. Ali Karimnezhad & Ahmad Parsian, 2014. "Robust Bayesian methodology with applications in credibility premium derivation and future claim size prediction," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 287-303, July.

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