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Best-possible bounds on the set of copulas with a given value of Spearman's footrule
Fuzzy Sets and Systems ( IF 3.2 ) Pub Date : 2020-11-20 , DOI: 10.1016/j.fss.2020.11.011
Gleb Beliakov , Enrique de Amo , Juan Fernández-Sánchez , Manuel Úbeda-Flores

In this paper we find pointwise best-possible bounds on the set of copulas with a given value of the Spearman's footrule coefficient. We show that the lower bound is always a copula but, unlike the bounds on sets of copulas with a given value of other measures, such as Kendall's tau, Spearman's rho and Blonqvist's beta, the upper bound can be a copula or a proper quasi-copula. We characterised both of these cases.



中文翻译:

具有给定 Spearman 规则值的 copula 集合的最佳可能边界

在本文中,我们在给定的 Spearman 脚规则系数值的情况下,找到了对 copula 集合的逐点最佳可能边界。我们证明下界总是一个 copula 但是,与具有给定其他度量值的 copula 集合的边界不同,例如 Kendall 的 tau、Spearman 的 rho 和 Blonqvist 的 beta,上限可以是一个 copula 或适当的准系词。我们描述了这两种情况。

更新日期:2020-11-20
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