Convergence of the Iterative Proportional Fitting Procedure

Abstract

The iterative proportional fitting procedure (IPFP) was introduced in 1940 by Deming and Stephan to estimate cell probabilities in contingency tables subject to certain marginal constraints. Its convergence and statistical properties have been investigated since then by several authors and by several different methods. A natural extension of the IPFP to the case of bivariate densities has been introduced by Ireland and Kullback. It has been conjectured that also in the general case the IPFP converges to the minimum discrimination projection on the class of distributions with given marginals. We verify this conjecture under some regularity conditions.