JSM 2005 Online Program

Abstract #304125

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Activity Number:	401
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
Sponsor:	General Methodology
Abstract - #304125
Title:	An Iterative Procedure for General Probability Measures To Obtain I-Projections onto Intersections of Convex Sets
Author(s):	Bhaskar Bhattacharya*+
Companies:	Southern Illinois University, Carbondale
Address:	Department of Mathematics, Carbondale, IL, 62901, United States
Keywords:	I-projection ; inequality constraints ; stochastic order ; convergence
Abstract:	The iterative proportional fitting procedure (IPFP) was introduced by Deming and Stephan in 1940. Later, for bivariate densities, this procedure was investigated by Kullback, Ruschendorf. 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 those 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 IPFP and marginal stochastic orders are worked out in this context.

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