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On the properties of some nonparametric concordance measures in the discrete case

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Mesfioui, M. Tajar, A

It is shown here that Kendall's tau and Spearman's rho are monotone with respect to the concordance ordering of pairs of discrete as well as continuous random variables. This extends and completes results of [Tchen, A.H., 1980, The Annals of Probability, 8, 814-827.] It is also shown that various relationships between Kendall's tau and Spearman's rho mentioned in [Nelsen, R.B., 1999, An Introduction to Copulas. Lecture Notes in Statistics no. 139 (New York: Springer).] remain valid for discrete variables. In particular, a result of [Caperaa, P. and Genest, C., 1993, Journal of Nonparametric Statistics, 2, 183-194.] is extended to the case of discrete random pairs. Finally, an analytic expression is given for the most extreme values of Kendall's tau and Spearman's rho associated with discrete uniform variates.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2005
Language Anglais
Journal information "Journal of Nonparametric Statistics" - Vol. 17, no. 5, p. 541-554 (2005)
Peer reviewed yes
Publisher Taylor & Francis Ltd (Abingdon)
issn 1048-5252
e-issn 1029-0311
Publication status Publié
Affiliation UCL
Keywords concordance measures ; concordance order ; Copulas ; dependence properties ; Frechet bounds ; monotone dependence
Links
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Bibliographic reference Mesfioui, M. ; Tajar, A. On the properties of some nonparametric concordance measures in the discrete case. In: Journal of Nonparametric Statistics, Vol. 17, no. 5, p. 541-554 (2005)
Permanent URL http://hdl.handle.net/2078.1/39308