Contingency tables with given marginals

Abstract

In its simplest formulation the problem considered is to estimate the cell probabilities Pij of an r × c contingency table for which the marginal probabilities Pi and Pj are known and fixed, so as to minimize ΣΣpij In (pij/πij), where πij are the corresponding entries in a given contingency table. An iterative procedure is given for determining the estimates and it is shown that the estimates are BAN, and that the iterative procedure is convergent. A summary of results for a four-way contingency table is given. An illustrative example is given.