Multi-way contingency tables with uniform margins

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...

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Bibliographic Details
Main Authors Perrone, Elisa, Fontana, Roberto, Rapallo, Fabio
Format Journal Article
LanguageEnglish
Published 05.04.2024
Subjects
Statistics - Methodology
Online AccessGet full text
DOI10.48550/arxiv.2404.04343

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Summary: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.
DOI:10.48550/arxiv.2404.04343