Convergence of the iterative proportional fitting procedure. (English) Zbl 0851.62038

Rüschendorf, Ludger

Ann. Stat. 23, No. 4, 1160-1174 (1995).

Summary: The iterative proportional fitting procedure (IPFP) was introduced by W. E. Deming and F. F. Stephan [Ann. Stat. 11, 427-444 (1940; Zbl 0024.05502)] 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 C. T. Ireland and S. Kullback [Biometrika 55, 179-188 (1968; Zbl 0155.26701)]. 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.

MSC:

62H17	Contingency tables
60F99	Limit theorems in probability theory
62B99	Sufficiency and information

Keywords:

\(I\)-projection; Kullback-Leibler distance; marginal adjustment; iterative proportional fitting procedure; cell probabilities; contingency tables; bivariate densities; minimum discrimination projection; given marginals

Citations:

Zbl 0024.05502; Zbl 0155.26701