JSM 2004 - Toronto

Abstract #300453

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Activity Number: 51
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract - #300453
Title: Mutual Information for the Multinomial Distribution
Author(s): Walfredo R. Javier*+ and Arjun K. Gupta
Companies: Southern University, Baton Rouge and Bowling Green State University
Address: Mathematics Dept., Baton Rouge, LA, 70813-9757,
Keywords: asymptotic distribution ; kullback-Leibler number ; mutual information ; multinomial distribution ; normal quadratic form
Abstract:

Mutual information, T(X), among the components of a q-variate random vector X is defined to be the expected value of the natural logarithm of the ratio of the joint density function and the product of the marginal densities of the component variables. This paper presents T(X) for the multinomial distribution. The sampling distribution of the maximum likelihood estimator of T(X) is derived as the distribution of a quadratic form from the approximating (q-1)-variate normal distribution; its characteristic function,mean and approximate variance are then computed. It is proposed to use this sampling distribution in inference problems involving the parameters of the multinomial distribution.

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