I-projections and Conditional Iterative Proportional Fitting

Résumé

The study of probability measures verifying prescribed marginal constraints is a wide topic, with many applications in statistics and has been extensively studied. In particular, the study of the problem of minimization on a set of prescribed marginal in the sense of relative entropy plays a basic role in the information theoric approach to statistics. I want first to present projections in relative entropy in the general case of convex sets, and the main results existing about it, then an algorithm which applies to the approximation problem linked to these projections in the marginal case. At the end, I will talk about the Gaussian version of this algorithm studied by Cramer, in which case I found a little result on the rate of convergence.