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In this paper the author investigates the problem of defining a multivariate dependence ordering. First, the author provides a characterization of the concordance dependence ordering between multivariate random vectors with fixed margins. Central to the characterization is a multivariate generalization of a well-known bivariate elementary dependence increasing rearrangement. Second, to order multivariate random vectors with non-fixed margins, the author imposes a scale invariance principle which leads to a copula-based concordance dependence ordering. Finally, a wide family of copula-based measures of dependence is characterized to which Spearman?s rank correlation coefficient belongs.
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