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A multivariate version of Gini’s rank association coefficient. (English) Zbl 1110.62081

Summary: We introduce a multivariate generalization of the population version of Gini’s rank association coefficient, giving a response to an open question posed by R. B. Nelsen [Concordance and copulas: a survey. C. Cuadras, J. Fortiana and J. A. Rodríguez (eds.), Distributions with given Marginals and Statistical Modelling. 169–178 (2002); see also J. Nonparametric Stat. 9, No. 3, 227–238 (1998; Zbl 0919.62057)]. We also study some properties of this version, present the corresponding results for the sample statistic, and provide several examples.

MSC:

62H20 Measures of association (correlation, canonical correlation, etc.)
62H05 Characterization and structure theory for multivariate probability distributions; copulas

Citations:

Zbl 0919.62057
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Full Text: DOI

References:

[1] Gini C. (1914). L’Ammontare e la composizione della ricchezza delle nazione. Bocca, Torino.
[2] Gould, H.W. (1972). Combinatorial Identities. Morgantown Printing and Binding Co., W. Va. · Zbl 0263.05013
[3] Nelsen, R.B. (1999). An Introduction to Copulas, Springer, New York. · Zbl 0909.62052
[4] Nelsen, R.B. (2002). Concordance and copulas: A survey. In: C. Cuadras, J. Fortiana, J.A. Rodríguez (Eds.), Distributions with Given Marginals and Statistical Modelling, Kluwer Academic Publishers, Dordrecht, pp. 169–178. · Zbl 1135.62337
[5] Úbeda-Flores, M. (2005). Multivariate versions of Blomqvist’s beta and Spearman’s footrule. Ann. Inst. Statist. Math. In press. · Zbl 1093.62060
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