An iterative procedure for general probability measures to obtain I-projections onto intersections of convex sets

• 成果类型: Article
• 署名作者: Bhattacharya, Bhaskar
• 署名单位: Southern Illinois University System; Southern Illinois University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000056
• 发表日期: 2006
• 页码: 878-902
• 关键词: log-linear models; contingency-tables; fitting procedure; Duality; INFORMATION; adjustment; MARGINALS

摘要

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 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 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.