Measures of association for approximating copulas

Fuente: arXiv
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Main Author: Rockel, Marcus
Format: Preprint
Published: 2025
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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