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

by   Rabi Bhattacharya, et al.

This article focuses on the performance of Bayes estimators, 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 space and rather large sample sizes.



There are no comments yet.


page 1

page 2

page 3

page 4


Nonparametric empirical Bayes estimation based on generalized Laguerre series

In this work, we delve into the nonparametric empirical Bayes theory and...

Minimaxity and Limits of Risks Ratios of Shrinkage Estimators of a Multivariate Normal Mean in the Bayesian Case

In this article, we consider two forms of shrinkage estimators of the me...

Bayesian Shrinkage Estimation of Negative Multinomial Parameter Vectors

The negative multinomial distribution is a multivariate generalization o...

Nonparametric estimation of multivariate copula using empirical bayes method

In the field of finance, insurance, and system reliability, etc., it is ...

Simultaneous Inference for Multiple Proportions: A Multivariate Beta-Binomial Model

In this work, the construction of an m-dimensional Beta distribution fro...

RKL: a general, invariant Bayes solution for Neyman-Scott

Neyman-Scott is a classic example of an estimation problem with a partia...

Bayes Linear Emulation of Simulated Crop Yield

The analysis of the output from a large scale computer simulation experi...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.