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.
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