Algebraic methods in contingency table analysis and discrete copulas

Perrone Elisa, Eindhoven University of Technology
Fontana Roberto, Politecnico di Torino
Rapallo Fabio, Università di Genova

We analyze the connection between contingency tables and copulas in a discrete framework. In particular, we study the relation between 2-way and multi-way contingency tables and discrete copulas in algebraic terms. We investigate under which conditions it is possible to associate a multi-way table to (1) a unique discrete copula or (2) a closed-form class of parametric discrete copulas. We illustrate the results by walking through examples and conclude with a discussion on the impact of structural zeros on the developed theory.

Area: IS19 - Dependence Modeling (Elisa Perrone)

Keywords: contingency tables, discrete copulas, odds ratios, structural zeros