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}
}
  • F. Komaki
  • Published 5 December 2011
  • Mathematics, Computer Science
  • arXiv: Statistics Theory
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… 
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