Quantifying Directed Dependence with Kendall’s Tau

The Limbach, C.Fuchs, S.Markov product of copulas is a powerful tool for modeling directed dependence between two random variables \(X\) and \(Y\) , and its evaluation via certain concordance measures such as Spearman’s rho and Spearman’s footrule allows for quantifying different aspects of directed dependence, and thus, different types of influence that \(X\) can exert on \(Y\) . Motivated by the recent publications [3, 11], we apply Kendall’s tau to the Markov product which leads to a dependence measure determining the degree of agreement among the conditional distributions of \(Y\) given \(X=x\) .