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Estimating Multinomial Cell Probabilities Under Quadratic Loss
Tapan K. Nayak and Dayanand N. Naik
Journal of the Royal Statistical Society. Series D (The Statistician)
Vol. 38, No. 1 (1989), pp. 3-10
Stable URL: http://www.jstor.org/stable/2349013
Page Count: 8
You can always find the topics here!Topics: Bayes estimators, Population estimates, Estimators, Maximum likelihood estimation, Statistical estimation, Mathematical functions, Statistics, Entropy, Probabilities, Proportions
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For estimating the cell probabilities of a multinomial distribution, a quadratic loss function based on the intrinsic differences among the categories is introduced. Such loss functions include many commonly used losses as special cases and can be interpreted as divergence measures induced by quadratic entropy. For this class of loss functions and a single population, the Bayes estimator, the minimax estimator and a pseudo-Bayes estimator are obtained. Also, for estimating the cell probabilities of several multinomial populations, empirical Bayes and pseudo-Bayes estimators are discussed and illustrated with an example.
Journal of the Royal Statistical Society. Series D (The Statistician) © 1989 Royal Statistical Society