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

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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.

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Acknowledgements

The authors are most grateful to the referees whose thoughtful comments led to a more comprehensive discussion of the subject. The first author also acknowledges the support of the Faculty of Economics and Management, Free University of Bozen–Bolzano, via the project NEW-DEMO.

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Authors and Affiliations

  1. Free University of Bozen–Bolzano, Bozen, Italy

    Sebastian Fuchs

  2. Technische Universität Dresden, Dresden, Germany

    Yann McCord & Klaus D. Schmidt

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  1. Sebastian Fuchs
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  2. Yann McCord
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  3. Klaus D. Schmidt
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Correspondence to Sebastian Fuchs.

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Fuchs, S., McCord, Y. & Schmidt, K.D. Characterizations of Copulas Attaining the Bounds of Multivariate Kendall’s Tau. J Optim Theory Appl 178, 424–438 (2018). https://doi.org/10.1007/s10957-018-1285-6

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  • DOI: https://doi.org/10.1007/s10957-018-1285-6

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