(Received September 8, 1994; revised May 20, 1996)
Abstract. Categorical data of high (but finite) dimensionality generate sparsely populated J-way contingency tables because of finite sample sizes. A model representing such data by a ``smooth'' low dimensional parametric structure using a ``natural'' metric would be useful. We discuss a model using a metric determined by convex sets to represent moments of a discrete distribution to order J. The model is shown, from theorems on convex polytopes, to depend only on the linear space spanned by the convex set--it is otherwise measure invariant. We provide an empirical example to illustrate the maximum likelihood estimation of parameters of a particular statistical application (Grade of Membership analysis) of such a model.
Key words and phrases: Probability mixtures, convex sets, polytopes, convex duality, Grades of Membership.
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