# Asymptotically minimax Bayesian predictive densities for multinomial models

@article{Komaki2011AsymptoticallyMB, title={Asymptotically minimax Bayesian predictive densities for multinomial models}, author={Fumiyasu Komaki}, journal={arXiv: Statistics Theory}, year={2011} }

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…

## 8 Citations

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The numerical experiments support the conjecture about non-achievability by so called last-step minimax algorithms, which are independent of n and show that in the multinomial model, a Bayes mixture dened by the conjugate Dirichlet prior with a simple dependency on n achieves asymptotic minimaxity for all sequences, thus providing a simpler asymptic minimax strategy compared to earlier work by Xie and Barron.

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The numerical experiments support the conjecture about non-achievability by so called last-step minimax algorithms, which are independent of n and show that in the multinomial model, a Bayes mixture defined by the conjugate Dirichlet prior with a simple dependency on n achieves asymptotic minimaxity for all sequences.

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