Title: Discrete copulas and stochastic monotonicity
Authors: Elisa Perrone - Eindhoven University of Technology (Netherlands) [presenting]
Abstract: Discrete copulas serve as useful tools for modeling dependence among random variables. The space of discrete copulas admits a representation as a convex polytope which has for instance been exploited in entropy-copula methods relevant to environmental sciences. We further analyze geometric features of discrete copulas with prescribed stochastic properties. In particular, we focus on studying geometrically the class of componentwise convex discrete copulas, i.e., ultramodular discrete copulas, which capture joint behavior of mutually stochastically decreasing random variables. First, we identify the minimal collection of bounding affine hyperplanes of the convex space of ultramodular discrete copulas. Then, we analyze some of the extremal points of the class. Finally, we show how our geometric findings can be used to conduct hypothesis testing for stochastic decreasingness of bivariate random vectors.