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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
Published by: Wiley for the Royal Statistical Society
DOI: 10.2307/2349013
Stable URL: http://www.jstor.org/stable/2349013
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Estimating Multinomial Cell Probabilities Under Quadratic Loss
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Abstract

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.

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