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

  • Kiapour, A.
  • Nematollahi, N.
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211002331
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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 81 (2011)
    Issue (Month): 11 (November)
    Pages: 1717-1724

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:11:p:1717-1724
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    1. 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.
    2. 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.
    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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