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

2019/10/05 by Rabi Bhattacharya, Rachel A. Oliver, Bhattacharya, Rabi +1
Computer Science · Mathematics · #62 #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1910.02316

openalex publication_date 2019/10/05 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

This article focuses on the performance of Bayes estimators, in comparison\nwith the MLE, in multinomial models with a relatively large number of cells.\nThe prior for the Bayes estimator is taken to be the conjugate Dirichlet, i.e.,\nthe multivariate Beta, with exchangeable distributions over the coordinates,\nincluding the non-informative uniform distribution. The choice of the\nmultinomial is motivated by its many applications in business and industry, but\nalso by its use in providing a simple nonparametric estimator of an unknown\ndistribution. It is striking that the Bayes procedure outperforms the\nasymptotically efficient MLE over most of the parameter spaces for even\nmoderately large dimensional parameter space and rather large sample sizes.\n

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