Concordance measures for multivariate non-continuous random vectors
AbstractA 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)  and Denuit and Lambert (2005) . 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 InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 101 (2010)
Issue (Month): 10 (November)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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.
- M. Taylor, 2007. "Multivariate measures of concordance," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(4), pages 789-806, December.
- Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
- 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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