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2012 Asymptotically minimax Bayesian predictive densities for multinomial models
Fumiyasu Komaki
Electron. J. Statist. 6(none): 934-957 (2012). DOI: 10.1214/12-EJS700

Abstract

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.

Citation

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Fumiyasu Komaki. "Asymptotically minimax Bayesian predictive densities for multinomial models." Electron. J. Statist. 6 934 - 957, 2012. https://doi.org/10.1214/12-EJS700

Information

Published: 2012
First available in Project Euclid: 25 May 2012

zbMATH: 1281.62036
MathSciNet: MR2988434
Digital Object Identifier: 10.1214/12-EJS700

Subjects:
Primary: 62C10, 62C20
Secondary: 62F15

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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