Schur convexity of the maximum likelihood function for the multivariate hypergeometric and multinomial distributions

Philip J. Boland and Frank Proschan

Statistics & Probability Letters, 1987, vol. 5, issue 5, 317-322

Abstract: We define for a family distributions p[theta](x), [theta] [epsilon] [Theta], the maximum likelihood function L at a sample point x by L(x) = sup[theta][epsilon][Theta]P[theta](x). We show that for the multivariate hypergeometric and multinomial families, the maximum likelihood function is a Schur convex function of x. In the language of majorization, this implies that the more diverse the elements or components of x are, the larger is the function L(x). Several applications of this result are given in the areas of parameter estimation and combinatorics. An improvement and generalization of a classical inequality of Khintchine is also derived as a consequence.

Keywords: maximum; likelihood; function; Schur; convexity; majorization; multivariate; hypergeometric; multinomial; Khintchine's; inequality (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (3)

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