Characterizations of Copulas Attaining the Bounds of Multivariate Kendall’s Tau
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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.
KeywordsKendall’s tau Measures of concordance Copulas Shuffles of copulas Countermonotonicity
Mathematics Subject Classification49J99 49K99
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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