Title: Geometric structure in dependence models and applications
Authors: Elisa Perrone - Eindhoven University of Technology (Netherlands) [presenting]
Abstract: The geometric properties of copulas are explored in order to address dependence modeling challenges in several applications, such as hydrology and finance. In particular, we study the class of discrete copulas, i.e., restrictions of copulas on uniform grid domains, which admits representations as convex polytopes. First, we give a geometric characterization of discrete copulas with desirable stochastic constraints in terms of the properties of their associated convex polytopes. In doing so, we draw connections to the popular Birkhoff polytopes, thereby unifying and extending results from both the statistics and the discrete geometry literature. Then, we further consolidate the statistics/discrete geometry bridge by showing the significance of our geometric findings to (1) construct entropy-copula models useful in hydrology, and (2) design test statistics for stochastic monotonicity properties of interest in finance. Finally, we discuss extension to analyze discrete copulas with positive dependence constraints, such as total positivity.