The exact region determined by Spearman's footrule, Gini's gamma and Kendall's tau

Abstract

Concordance measures are used to express the degree of association between random variables. Practitioners may use several distinct concordance measures to narrow the space of possible dependence structures. Consequently, the relations between different (weak) concordance measures have been extensively studied in recent years. The goal of this paper is to study the relation between Kendall's tau, Gini's gamma and Spearman's footrule. In particular, we describe the exact region determined by these three measures, using shuffles of $M$ and ordinal sums of copulas. We also provide the formulas for five main (weak) concordance measures and Chatterjee's xi of ordinal sums of copulas.

arXiv comment24 pages, 5 figures

References in corpus (4)

• On the exact region determined by Kendall's tau and Spearman's rho
• Spearman's footrule and Gini's gamma: Local bounds for bivariate copulas and the exact region with respect to Blomqvist's beta
• On the exact region determined by Spearman's rho and Spearman's footrule
• The exact region and an inequality between Chatterjee's and Spearman's rank correlations