Convex models of high dimensional discrete data

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.

Duke Scholars

Author Kenneth G. Manton Trinity College of Arts & Sciences