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Journal of Optimization Theory and Applications

, Volume 178, Issue 2, pp 424–438 | Cite as

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

  • Sebastian Fuchs
  • Yann McCord
  • Klaus D. Schmidt
Article

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.

Keywords

Kendall’s tau Measures of concordance Copulas Shuffles of copulas Countermonotonicity 

Mathematics Subject Classification

49J99 49K99 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Free University of Bozen–BolzanoBozenItaly
  2. 2.Technische Universität DresdenDresdenGermany

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