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Multivariate versions of Blomqvist’s beta and Spearman’s footrule. (English) Zbl 1093.62060
Summary: We define multivariate versions of the medial correlation coefficient and the rank correlation coefficient Spearman’s footrule in terms of copulas. We also present corresponding results for the sample statistic and provide a comparison of lower bounds among different measures of multivariate association.

MSC:
62H20 Measures of association (correlation, canonical correlation, etc.)
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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[1] Blomqvist, N. (1950). On a measure of dependence between two random variables,Annals of Mathematical Statistics,21, 593–600. · Zbl 0040.22403
[2] Nelsen, R. B. (1993). Some concepts of bivariate symmetry,Nonparametric Statistics,3, 95–101. · Zbl 1380.62227
[3] Nelsen, R. B. (1996). Nonparametric Measures of Multivariate Association,Distributions with Fixed Marginals and Related Topics (eds. L. Rüschendorf, B. Schweizer and M. D. Taylor), 223–232, IMS Lecture Notes-Monograph Series, No. 28, Hayward, California.
[4] Nelsen, R. B. (1999).An Introduction to Copulas, Springer, New York. · Zbl 0909.62052
[5] Nelsen, R. B. (2002). Concordance and copulas: A survey,Distributions with Given Marginals and Statistical Modelling (eds. C. Cuadras, J., Fortiana and J. A. Rodríguez), 169–178, Kluwer Academic Publishers, Dordrecht. · Zbl 1135.62337
[6] Nelsen, R. B. and Úbeda-Flores, M. (2004). A comparison of bounds on sets of joint distribution functions derived from various measures of association,Communications in Statistics–Theory and Methods,33, 2299–2305. · Zbl 1210.62054
[7] Rodríguez-Lallena, J. A. and Úbeda-Flores, M. (2004). Best-possible bounds on sets of multivariate distribution functions,Communications in Statistics–Theory and Methods,33, 805–820. · Zbl 1066.62056
[8] Spearman, C. (1906) ’Footrule’ for measuring correlation,British Journal of Psychology,2, 89–108.
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