Multi-way contingency tables with uniform margins
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910400147095552 |
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| author | Perrone, Elisa Fontana, Roberto Rapallo, Fabio |
| author_facet | Perrone, Elisa Fontana, Roberto Rapallo, Fabio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-way contingency tables with uniform margins Perrone, Elisa Fontana, Roberto Rapallo, Fabio Methodology 62H17, 62H05 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. |
| title | Multi-way contingency tables with uniform margins |
| topic | Methodology 62H17, 62H05 |
| url | https://arxiv.org/abs/2404.04343 |