A1477
Title: An algorithmic procedure for solving the generalized minimum information checkerboard copula problem
Authors: Ivan Kojadinovic - CNRS UMR 5142 LMA University of Pau (France) [presenting]
Tommaso Martini - University of Torino (Italy)
Abstract: The minimum information copula principle (see Meeuwissen and Bedford, 1997) is a maximum entropy-like approach for finding the least informative copula that satisfies a certain number of expectation constraints specified either from expert knowledge or the available limited data. In this presentation, we first propose a generalization of this principle allowing the inclusion of additional constraints fixing certain higher-order margins of the copula. We next prove that the associated optimization problem has a unique solution under a natural condition. As the latter problem is intractable in general, following the existing literature, we consider its version with all the probability measures involved in its formulation replaced by checkerboard approximations. This amounts to attempting to solve a so-called discrete I-projection linear problem. We then use the seminal results of Csiszar (1975) to derive an IPFP-like procedure for solving the latter and provide theoretical guarantees for its convergence. We conclude the presentation with numerical experiments in dimensions up to four with substantially finer discretizations than those encountered in the literature.
