近似copula的关联度量
Measures of association for approximating copulas
AI总结：
研究用于近似目的的多种copula关联度量的闭式表达式，包括Bernstein、shuffle-of-min、checkerboard和check-min copula，并证明对于具有TP2密度的绝对连续二元copula C及其近似n×n棋盘copula Cn，有ξ(Cn) ≤ ξ(C)且当n→∞时ξ(Cn)→ξ(C)。
摘要：
本文研究了常用于近似目的的多种copula关联度量的闭式表达式，包括Bernstein、shuffle-of-min、checkerboard和check-min copula。特别地，提供了最近流行的Chatterjee's ξ的闭式表达式，该度量量化了两个随机变量之间的依赖性。给定一个具有TP2密度的绝对连续二元copula C及其近似n×n棋盘copula Cn，我们证明ξ(Cn) ≤ ξ(C)且当n→∞时ξ(Cn)→ξ(C)。
英文摘要：
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 $n\to\infty$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
