2024/04/05 by Perrone, Elisa, Fontana, Roberto, Rapallo, Fabio
#62H05 #62H17 #FOS: Computer and information sciences #Methodology (stat.ME)
paper · doi:10.48550/arxiv.2404.04343
We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. Such a problem relates to recent developments in copula modeling for discrete random vectors. Here, we focus on three-way binary tables and show that, even in such a simple case, the situation is quite different than for two-way tables. Many more constraints are needed to ensure a unique solution to the problem. Therefore, the uniqueness of the transformed table is subject to arbitrary choices of the practitioner. We illustrate the theory through some examples, and conclude with a discussion on the topic and future research directions.