An empirical bayes estimate of multinomial probabilities |
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Authors: | Khursheed Alam Amitava Mitra |
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Institution: | 1. Departmetn of Mathematical Sciences , Clemson University , Clemson, South Carolina, 29634;2. Departmetn of Management , Auburn University , Auburn, Alabama, 36849 |
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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. |
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Keywords: | multinomial distribution maximum likelihood empirical bayes quadratic loss |
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