Copula-based dependence measures

The aim of the present paper is to examine two wide classes of dependence coefficients including several well-known coefficients, for example Spearman's rho, Spearman's footrule, and the Gini coefficient. There is a close relationship between the two classes: The second class is obtained by a symmetrisation of the coefficients in the former class. The coefficients of the first class describe the deviation from monotonically increasing dependence. The construction of the coefficients can be explained by geometric arguments. We introduce estimators of the dependence coefficients and prove their asymptotic normality.