Electronic Journal of Statistics

Asymptotically minimax Bayesian predictive densities for multinomial models

Fumiyasu Komaki

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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.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 934-957.

Dates
First available in Project Euclid: 25 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1337951629

Digital Object Identifier
doi:10.1214/12-EJS700

Mathematical Reviews number (MathSciNet)
MR2988434

Zentralblatt MATH identifier
1281.62036

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures 62C20: Minimax procedures
Secondary: 62F15: Bayesian inference

Keywords
Dirichlet prior Jeffreys prior Kullback-Leibler divergence latent information prior reference prior

Citation

Komaki, Fumiyasu. Asymptotically minimax Bayesian predictive densities for multinomial models. Electron. J. Statist. 6 (2012), 934--957. doi:10.1214/12-EJS700. https://projecteuclid.org/euclid.ejs/1337951629


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