On the exact region determined by Spearman's rho and Spearman's footrule

Abstract

We determine the lower bound for possible values of Spearman's rho of a bivariate copula given that the value of its Spearman's footrule is known and show that this bound is always attained. We also give an estimate for the exact upper bound and prove that the estimate is attained for some but not all values of Spearman's footrule. Nevertheless, we show that the estimate is quite tight.

32 pages

References in corpus (1)

• Spearman's footrule and Gini's gamma: Local bounds for bivariate copulas and the exact region with respect to Blomqvist's beta

Cited by in corpus (2)

• The exact region and an inequality between Chatterjee's and Spearman's rank correlations
• The exact region determined by Spearman's footrule, Gini's gamma and Kendall's tau