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Asymptotically minimax Bayesian predictive densities for multinomial models. (English) Zbl 1281.62036
Summary: One-step ahead prediction for the multinomial model is considered. The performance of a predictive density is evaluated by the average Kullback-Leibler divergence from the true density to the predictive density. Asymptotic approximations of risk functions of Bayesian predictive densities based on Dirichlet priors are obtained. It is shown that a Bayesian predictive density based on a specific Dirichlet prior is asymptotically minimax. The asymptotically minimax prior is different from known objective priors such as the Jeffreys prior or the uniform prior.
MSC:
62C10 Bayesian problems; characterization of Bayes procedures
62C20 Minimax procedures in statistical decision theory
62F15 Bayesian inference
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