Minimum Information Copulas and Related Topics

Abstract

A minimum information copula is a copula that is closest to the independent one under given moment restrictions. The obtained class is interpreted as a copula version of exponential families and is mathematically of interest. In this paper, we review the definition and fundamental properties together with concrete examples. In particular, we overview its relationship with information geometry, matrix scaling and optimal transport theoryvia discrete approximation of copulas. Estimation methods of parameters are also discussed.