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April 2006 An iterative procedure for general probability measures to obtain I-projections onto intersections of convex sets
Bhaskar Bhattacharya
Ann. Statist. 34(2): 878-902 (April 2006). DOI: 10.1214/009053606000000056

Abstract

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 Rüschendorf. 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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Bhaskar Bhattacharya. "An iterative procedure for general probability measures to obtain I-projections onto intersections of convex sets." Ann. Statist. 34 (2) 878 - 902, April 2006. https://doi.org/10.1214/009053606000000056

Information

Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1117.62003
MathSciNet: MR2283396
Digital Object Identifier: 10.1214/009053606000000056

Subjects:
Primary: 60B10, 62B10, 65K10
Secondary: 60E15

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 2 • April 2006
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