Extreme values of the mass distribution associated with $d$-quasi-copulas via linear programming
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912369029939200 |
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| author | Belšak, Matej Omladič, Matjaž Vuk, Martin Zalar, Aljaž |
| author_facet | Belšak, Matej Omladič, Matjaž Vuk, Martin Zalar, Aljaž |
| contents | The recent survey published in Fuzzy Sets and Systems nicknamed ``Hitchhiker's Guide'' has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. Some of the open problems listed there were solved, and some conjectured one way or the other. This paper concentrates on the Open Problem 5 of this list concerning bounds on the volume of a $d$--variate quasi-copula. We disprove a recent conjecture published in the same journal on the lower bound of this volume. We also give evidence that the problem is much more difficult than suspected and provide hints about its final solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extreme values of the mass distribution associated with $d$-quasi-copulas via linear programming Belšak, Matej Omladič, Matjaž Vuk, Martin Zalar, Aljaž Statistics Theory 62H05, 60A99, 60E05, 26B35 The recent survey published in Fuzzy Sets and Systems nicknamed ``Hitchhiker's Guide'' has raised the rating of quasi-copula problems in the dependence modeling community in spite of the lack of statistical interpretation of quasi-copulas. Some of the open problems listed there were solved, and some conjectured one way or the other. This paper concentrates on the Open Problem 5 of this list concerning bounds on the volume of a $d$--variate quasi-copula. We disprove a recent conjecture published in the same journal on the lower bound of this volume. We also give evidence that the problem is much more difficult than suspected and provide hints about its final solution. |
| title | Extreme values of the mass distribution associated with $d$-quasi-copulas via linear programming |
| topic | Statistics Theory 62H05, 60A99, 60E05, 26B35 |
| url | https://arxiv.org/abs/2410.19339 |