On the properties of some nonparametric concordance measures in the discrete case
(2005) Journal of Nonparametric Statistics — Vol. 17, n° 5, p. 541-554 (2005)
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- Abstract
- 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.
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Mesfioui, M., & Tajar, A. (2005). On the properties of some nonparametric concordance measures in the discrete case. Journal of Nonparametric Statistics, 17(5), 541-554. https://doi.org/10.1080/10485250500038967 (Original work published 2005)