Mathematics – Statistics Theory
Scientific paper
2006-07-03
Annals of Statistics 2006, Vol. 34, No. 2, 878-902
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053606000000056 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053606000000056
The iterative proportional fitting procedure (IPFP) was introduced formally by Deming and Stephan in 1940. For bivariate densities, this procedure has been investigated by Kullback and R\"{u}schendorf. It is well known that the IPFP is a sequence of successive I-projections onto sets of probability measures with fixed marginals. However, when finding the I-projection onto the intersection of arbitrary closed, convex sets (e.g., marginal stochastic orders), a sequence of successive I-projections onto these sets may not lead to the actual solution. Addressing this situation, we present a new iterative I-projection algorithm. Under reasonable assumptions and using tools from Fenchel duality, convergence of this algorithm to the true solution is shown. The cases of infinite dimensional IPFP and marginal stochastic orders are worked out in this context.
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