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Deming and Stephan (1940) first proposed the use of an iterative proportional fitting procedure to estimate cell probabilities in a contingency table subject to certain marginal constraints. In this paper we first relate this procedure to a variety of sources and a variety of statistical problems. We then describe the procedure geometrically for two-way contingency tables using the concepts presented in Fienberg (1968). This geometrical description leads to a rather simple proof of the convergence of the iterative procedure. We conclude the paper with a discussion of extensions to multi-dimensional tables and to tables with some zero entries.
Stephen E. Fienberg (Mon,) studied this question.