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Kendall's tau and Spearman's rho for n -dimensional Archimedean copulas and their asymptotic properties

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  • Włodzimierz Wysocki

Abstract

We derive formulas for the dependence measures and for Archimedean n -copulas. These measures are n -dimensional analogues of the popular nonparametric dependence measures: Kendall's tau and Spearman's rho. For we obtain two formulas, both involving integrals of univariate functions. The formulas for 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 and , for a sequence 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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  • Włodzimierz Wysocki, 2015. "Kendall's tau and Spearman's rho for n -dimensional Archimedean copulas and their asymptotic properties," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 442-459, December.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:4:p:442-459
    DOI: 10.1080/10485252.2015.1070849
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    2. Gijbels Irène & Matterne Margot, 2021. "Study of partial and average conditional Kendall’s tau," Dependence Modeling, De Gruyter, vol. 9(1), pages 82-120, January.

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