Superiority of Bayes estimators over the MLE in high dimensional multinomial models and its implication for nonparametric Bayes theory
AffiliationUniv Arizona, Dept Math
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CitationBhattacharya, R., & Oliver, R. (2020). Superiority of Bayes estimators over the MLE in high dimensional multinomial models and its implication for nonparametric Bayes theory. Computational Statistics & Data Analysis, 107011. https://doi.org/10.1016/j.csda.2020.107011
Rights© 2020 Elsevier B.V. All rights reserved.
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AbstractThe performance of Bayes estimators is examined, in comparison with 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 the multinomial is motivated by its many applications in business and industry, but also by its use in providing a simple nonparametric estimator of an unknown distribution. It is striking that the Bayes procedure outperforms the asymptotically efficient MLE over most of the parameter spaces for even moderately large dimensional parameter spaces and rather large sample sizes. (C) 2020 Elsevier B.V. All rights reserved.
Note24 month embargo; published online: 15 May 2020
VersionFinal accepted manuscript