Abstract

(Under the direction of Barry H. Margolin) We investigate certain inferential aspects of mixtures of multinomial distributions, both in nonparametric and parametric contexts. As a nonparametric mixture model we propose a k-population finite mixture of binomial distributions, which can be applied to the analysis of noniid data generated from a series of toxicological experiments. A necessary and sufficient identifiability condition for the k-population finite mixture of binomials is obtained. The maximum likelihood estimates (MLE's) of the k-population finite mixture of binomials is computed via the EM algorithm (Dempster, Laird and Rubin, 1977), and the asymptotic properties of the MLE's are discussed. The identifiability condition is equivalent to the positive definiteness of the information matrix for the parameters. The MLE's and their sampling distributions, together with the data mentioned above, provide an empirical check of the statistical procedures proposed by Margolin, Kaplan and Zeiger (1981).

Citations