Estimating multinomial cell probabilities under quadratic loss

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 probabili- ties of several multinomial populations, empirical Bayes and pseudo-Bayes estimators are discussed and illustrated with an example.