An empirical bayes estimate of multinomial probabilities

Abstract

This paper deals with the prblem of estimating simultaneously the parameters (Cell probabilities) of m ≤ 2 independent multinomial distributions, with respect to a quadratic loss functions. An empirical Bayes estimator is proposed which is shown to have smaller risk than the maximum likelihood estimator for sufficiently large values of mq, where q is a measure of the average diversity of the given multinomial populations. Some numerical results are given on the performance of the proposed estimator.

Keywords:

• multinomial distribution
• maximum likelihood
• empirical bayes
• quadratic loss