Abstract
If X and Y are random variables with joint distribution function H, their dependence may be measured by Kendall’s tau, τ(X,Y), expressed as 4E(V) — 1 in terms of the random quantity V = H(X,Y) with distribution K on the interval [0,1]. A new dependence ordering based on K is defined and studied; although it does not always imply the classical positive quadrant dependence ordering, it is shown to be weaker than the association ordering of (1987) under weak regularity conditions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barbe, P., C. Genest, K. Ghoudi and B. Rémillard (1996). On Kendall’s process. Journal of Multivariate Analysis, 58, 197–229.
Block, H. W., D. Chhetry, Z. Fang and A. R. Sampson (1990). Partial orders on permutations and dependence orderings on bivariate empirical distributions. The Annals of Statistics, 18, 1840–1850.
Genest, C. and R. J. MacKay (1986). Copules archimédiennes et familles de lois tridimensionnelles dont les marges sont données. The Canadian Journal of Statistics, 14, 145–159.
Genest, C. and L.-P. Rivest (1993). Statistical inference procedures for Divariate Archimedean copulas. Journal of the American Statistical Association, 88, 1034–1043.
Joe, H. (1990). Multivariate concordance. Journal of Multivariate Analysis, 35, 12–30.
Khoudraji, A. (1995). Contributions à l’étude des copules et à la modélisation de valeurs extrêmes bivariées. Unpublished doctoral dissertation, Université Laval, Québec, Canada.
Pickands, J. (1981). Multivariate extreme value distributions. Bulletin of the International Statistical Institute, 859–78.
Schriever, B. F. (1987). An ordering of positive dependence. The Annals of Statistics, 15, 1208–1214.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Capéraà, P., Fougères, AL., Genest, C. (1997). A Stochastic Ordering Based on a Decomposition of Kendall’s Tau. In: Beneš, V., Štěpán, J. (eds) Distributions with given Marginals and Moment Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5532-8_9
Download citation
DOI: https://doi.org/10.1007/978-94-011-5532-8_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6329-6
Online ISBN: 978-94-011-5532-8
eBook Packages: Springer Book Archive