×

zbMATH — the first resource for mathematics

Multivariate measures of concordance. (English) Zbl 1131.62054
Summary: M. Scarsini [On measures of concordance. Stochastica 8, 201–218 (1984; Zbl 0582.62047)] introduced a set of axioms for measures of concordance of ordered pairs of continuous random variables. We exhibit an extension of these axioms to ordered \(n\)-tuples of continuous random variables, \(n \geq 2\). We derive simple properties of such measures, give examples, and discuss the relation of the extended axioms to multivariate measures of concordance previously discussed in the literature.

MSC:
62H20 Measures of association (correlation, canonical correlation, etc.)
62A01 Foundations and philosophical topics in statistics
PDF BibTeX XML Cite
Full Text: DOI Link
References:
[1] Dolati, A., Úbeda Flores, M. (2004). A multivariate version of Gini’s rank associate coefficient. Statistical Papers (in press). · Zbl 1110.62081
[2] Dolati, A., Úbeda Flores, M. (2006). On measures of concordance. Journal of Probability and Statistical Sciences (in press). · Zbl 1143.62321
[3] Edwards, H. (2004). Measures of concordance of polynomial type. Ph.D. dissertation, University of Central Florida.
[4] Edwards H., Mikusiński P., Taylor M.D. (2004). Measures of concordance determined by D 4-invariant copulas. International Journal of Mathematics and Mathematical Sciences 70:3867–3875 · Zbl 1075.62042
[5] Edwards H., Mikusiński P., Taylor M.D. (2005). Measures of concordance determined by D 4-invariant meaures on (0,1)2. Proceedings of the American Mathematical Society 133:1505–1513 · Zbl 1081.62032
[6] Hays W.L. (1960). A note on average tau as a measure of concordance. Journal of the American Statistical Association 55:331–341 · Zbl 0212.22403
[7] Kimeldorf G., Sampson A.R. (1987). Positive dependence orders. Annals of the Institute of Statistical Mathematics 39 (Part A):113–128 · Zbl 0617.62006
[8] Kimeldorf G., Sampson A.R. (1989). A framework for positive dependence. Annals of the Institute of Statistical Mathematics 41(1):31–45 · Zbl 0701.62061
[9] Joe H. (1990). Multivariate concordance. Journal of Multivariate Analysis 35:12–30 · Zbl 0741.62061
[10] Joe H. (1997). Multivariate models and dependence concepts. Chapman & Hall/CRC, Boca Raton · Zbl 0990.62517
[11] Nelsen R.B. (1999). An introduction to copulas. Springer, Berlin Heidelberg New York · Zbl 0909.62052
[12] Nelsen R.B. (2002). Concordance and copulas: A survey. In: Cuadras C.M., Fortiana J., Rodriguez-Lallena J.A. (eds) Distributions with given marginals and statistical modelling. Kluwer, Dordrecht, pp.169–177 · Zbl 1135.62337
[13] Scarsini M. (1984). On measures of concordance. Stochastica. VIII:201–218 · Zbl 0582.62047
[14] Schweizer B. Sklar A. (1983). Probabilistic metric spaces. North-Holland, New York · Zbl 0546.60010
[15] Tricomi, F. G. (1954). Tables of Integral Transforms, In: Based in part on notes left by Harry Bateman. vol.1 New York: McGraw-Hill. · Zbl 0058.34103
[16] Úbeda Flores M. (2005). Multivariate versions of Blomqvist’s beta and Spearman’s footrule. Annals of the Institute of Statistical Mathematics 57:781–788 · Zbl 1093.62060
[17] Zwillenger D. (2002). Standard mathematical tables and formulae, 31st Ed. CRC, Boca Raton
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.