Robust Bayesian prediction and estimation under a squared log error loss function
AbstractRobust 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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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 81 (2011)
Issue (Month): 11 (November)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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.
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