Measures of association for approximating copulas
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911708858023936 |
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| author | Rockel, Marcus |
| author_facet | Rockel, Marcus |
| contents | This paper studies closed-form expressions for multiple association measures of copulas commonly used for approximation purposes, including Bernstein, shuffle--of--min, checkerboard and check--min copulas. In particular, closed-form expressions are provided for the recently popularized Chatterjee's $ξ$, which quantifies the dependence between two random variables. Given an absolutely continuous bivariate copula $C$ with TP$_2$ density and approximating $n\times n$-checkerboard copula $C_n$, we show that $ξ(C_n) \le ξ(C)$ with $ξ(C_n) \to ξ(C)$ as $n\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measures of association for approximating copulas Rockel, Marcus Statistics Theory This paper studies closed-form expressions for multiple association measures of copulas commonly used for approximation purposes, including Bernstein, shuffle--of--min, checkerboard and check--min copulas. In particular, closed-form expressions are provided for the recently popularized Chatterjee's $ξ$, which quantifies the dependence between two random variables. Given an absolutely continuous bivariate copula $C$ with TP$_2$ density and approximating $n\times n$-checkerboard copula $C_n$, we show that $ξ(C_n) \le ξ(C)$ with $ξ(C_n) \to ξ(C)$ as $n\to\infty$. |
| title | Measures of association for approximating copulas |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2505.08045 |