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This article focuses on the performance of Bayes estimators, in comparisonwith the MLE, in multinomial models with a relatively large number of cells.The prior for the Bayes estimator is taken to be the conjugate Dirichlet, i.e.,the multivariate Beta, with exchangeable distributions over the coordinates,including the non-informative uniform distribution. The choice of themultinomial is motivated by its many applications in business and industry, butalso by its use in providing a simple nonparametric estimator of an unknowndistribution. It is striking that the Bayes procedure outperforms theasymptotically efficient MLE over most of the parameter spaces for evenmoderately large dimensional parameter space and rather large sample sizes.

Superiority of Bayes estimators over the MLE in high dimensional multinomial models and its implication for nonparametric Bayes theory