文章基本信息

标题：Intrinsic posterior regret gamma-minimax estimation for the exponential family of distributions
本地全文：下载
作者：Mohammad Jafari Jozani ; Nahid Jafari Tabrizi
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2013
卷号：7
页码：1856-1874
DOI：10.1214/13-EJS828
语种：English
出版社：Institute of Mathematical Statistics
摘要：In practice, it is desired to have estimates that are invariant under reparameterization. The invariance property of the estimators helps to formulate a unified solution to the underlying estimation problem. In robust Bayesian analysis, a frequent criticism is that the optimal estimators are not invariant under smooth reparameterizations. This paper considers the problem of posterior regret gamma-minimax (PRGM) estimation of the natural parameter of the exponential family of distributions under intrinsic loss functions with Kullback-Leibler distance. We show that under the class of Jeffrey’s Conjugate Prior (JCP) distributions, PRGM estimators are invariant to smooth one-to-one reparameterizations. We apply our results to several distributions and different classes of JCP, as well as the usual conjugate prior distributions. We observe that, in many cases, invariant PRGM estimators in the class of JCP distributions can be obtained by some modifications of PRGM estimators in the usual class of conjugate priors. Moreover, when the class of priors are convex or dependant on a hyper-parameter belonging to a connected set, we show that the PRGM estimator under the intrinsic loss function could be Bayes with respect to a prior distribution in the original prior class. Theoretical results are supplemented with several examples and illustrations.
关键词：Intrinsic loss function;Bayes estimator;robust Bayesian analysis;posterior risk;posterior regret gamma-minimax.