We derive formulas for the dependence measures τ n and ρ (1) n , ρ (2) n for Archimedean n-copulas. These measures are n-dimensional analogues of the popular nonparametric dependence measures: Kendall's tau and Spearman's rho. For τ n we obtain two formulas, both involving integrals of univariate functions. The formulas for ρ (1) n , ρ (2) n involve integrals of n-variate functions. We also obtain formulas for the three measures for copulas whose additive generators have completely monotone inverses. These formulas feature integrals of 2-variate functions (we use the Laplace transform). We study the asymptotic properties of the sequences (τ n (C n )) and (ρ (1) n (C n )), (ρ (2) n (C n )) for a sequence (C n ) of Archimedean copulas with a common additive generator. We also investigate the limit of this sequence, which is an infinite-dimensional copula on the Hilbert cube.
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