The W -footrule coefficient: a copula-based measure of countermonotonicity

We introduce the W-footrule coefficient ΦC, a copula-based coefficient of negative association defined as the L1-distance to the countermonotonic copula W. We prove that Gini's gamma admits the decomposition γC=23(φC+ΦC), linking it to Spearman's footrule φC. A rank-based estimator is introduced, with its strong consistency and asymptotic normality established via the functional delta method. Monte Carlo simulations confirm the estimator's finite-sample validity and its sensitivity to negative dependence structures.