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Concordance measures for multivariate non-continuous random vectors

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  • Mesfioui, Mhamed
  • Quessy, Jean-François
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    Abstract

    A notion of multivariate concordance suitable for non-continuous random variables is defined and many of its properties are established. This allows the definition of multivariate, non-continuous versions of Kendall's tau, Spearman's rho and Spearman's footrule, which are concordance measures. Since the maximum values of these association measures are not +1 in general, a special attention is given to the computation of upper bounds. The latter turn out to be multivariate generalizations of earlier findings made by Neslehová (2007) [9] and Denuit and Lambert (2005) [2]. They are easy to compute and can be estimated from a data set of (possibly) discontinuous random vectors. Corrected versions are considered as well.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 101 (2010)
    Issue (Month): 10 (November)
    Pages: 2398-2410

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    Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2398-2410

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    Keywords: Discontinuous distributions Copula Kendall's tau Multivariate concordance Spearman's rho Spearman's footrule;

    References

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    1. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    2. M. Taylor, 2007. "Multivariate measures of concordance," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(4), pages 789-806, December.
    3. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
    4. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    5. Manuel Úbeda-Flores, 2005. "Multivariate versions of Blomqvist’s beta and Spearman’s footrule," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(4), pages 781-788, December.
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    Cited by:
    1. Genest, Christian & Nešlehová, Johanna G. & Rémillard, Bruno, 2013. "On the estimation of Spearman’s rho and related tests of independence for possibly discontinuous multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 214-228.

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