On the choice of flattening constants for estimating multinomial probabilities

Stephen E. Fienberg and Paul W. Holland

Journal of Multivariate Analysis, 1972, vol. 2, issue 1, 127-134

Abstract: Bayesian estimation of the cell probabilities for the multinomial distribution (under a symmetric Dirichlet prior) leads to the use of a flattening constant [alpha] to smooth the raw cell proportions. The unsmoothed estimator corresponds to [alpha] = 0. The risk functions (under quadratic loss) of the Bayesian estimators for [alpha] > 0 are compared to that for [alpha] = 0 and this leads to an interpretation of any given choice of [alpha] > 0 in terms of the maximum number of "small" cell probabilities for which the corresponding smoothed estimator has smaller risk than the unsmoothed estimator. A real set of data is used to illustrate our interpretation of three a priori and three empirically determined choices of [alpha] that have appeared in the literature.

Keywords: Bayesian; estimation; Multinomial; flattening; constant; Dirichlet; prior; Risk; Loss (search for similar items in EconPapers)
Date: 1972
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Citations: View citations in EconPapers (4)

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