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Characterizations of Copulas Attaining the Bounds of Multivariate Kendall’s Tau

Author

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  • Sebastian Fuchs

    (Free University of Bozen–Bolzano)

  • Yann McCord

    (Technische Universität Dresden)

  • Klaus D. Schmidt

    (Technische Universität Dresden)

Abstract

Kendall’s tau is one of the most popular measures of concordance, and even in the multivariate case exact upper and lower bounds of Kendall’s tau are known. The present paper provides characterizations of the copulas attaining the bounds of multivariate Kendall’s tau, mainly in terms of the copula measure, but also via Kendall’s distribution function and for shuffles of copulas.

Suggested Citation

  • Sebastian Fuchs & Yann McCord & Klaus D. Schmidt, 2018. "Characterizations of Copulas Attaining the Bounds of Multivariate Kendall’s Tau," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 424-438, August.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:2:d:10.1007_s10957-018-1285-6
    DOI: 10.1007/s10957-018-1285-6
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    References listed on IDEAS

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    1. Durante, Fabrizio & Fernández-Sánchez, Juan, 2010. "Multivariate shuffles and approximation of copulas," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1827-1834, December.
    2. Manuel Úbeda-Flores, 2005. "Multivariate versions of Blomqvist’s beta and Spearman’s footrule," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 781-788, December.
    3. Lee, Woojoo & Ahn, Jae Youn, 2014. "On the multidimensional extension of countermonotonicity and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 68-79.
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    Cited by:

    1. Fuchs Sebastian & McCord Yann, 2019. "On the lower bound of Spearman’s footrule," Dependence Modeling, De Gruyter, vol. 7(1), pages 126-132, January.
    2. Jae Youn Ahn & Sebastian Fuchs, 2020. "On Minimal Copulas under the Concordance Order," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 762-780, March.
    3. Fuchs, Sebastian & Schmidt, Klaus D., 2021. "On order statistics and Kendall’s tau," Statistics & Probability Letters, Elsevier, vol. 169(C).

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