Convex lineability in copula and quasi-copula sets
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914311292583936 |
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| author | de Amo, Enrique Fernández-Sánchez, Juan García-Fernández, David Úbeda-Flores, Manuel |
| author_facet | de Amo, Enrique Fernández-Sánchez, Juan García-Fernández, David Úbeda-Flores, Manuel |
| contents | In this paper, we investigate several subsets of $n$-copulas and $n$-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain extremely large algebraic structures, namely linearly independent sets of cardinality of the continuum whose convex hull, and in some cases a closed convex linearly independent subset, remain entirely inside the class under study. These include the families of asymmetric copulas, copulas with maximal asymmetric measure, and proper $n$-quasi-copulas, among others. In contrast, for several other natural classes of copulas we show that (maximal) convex lineability holds while convex spaceability remains an open problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06918 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex lineability in copula and quasi-copula sets de Amo, Enrique Fernández-Sánchez, Juan García-Fernández, David Úbeda-Flores, Manuel Statistics Theory In this paper, we investigate several subsets of $n$-copulas and $n$-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain extremely large algebraic structures, namely linearly independent sets of cardinality of the continuum whose convex hull, and in some cases a closed convex linearly independent subset, remain entirely inside the class under study. These include the families of asymmetric copulas, copulas with maximal asymmetric measure, and proper $n$-quasi-copulas, among others. In contrast, for several other natural classes of copulas we show that (maximal) convex lineability holds while convex spaceability remains an open problem. |
| title | Convex lineability in copula and quasi-copula sets |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2602.06918 |