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Multivariate conditional versions of Spearman’s rho and related measures of tail dependence. (English) Zbl 1116.62061
Summary: A new family of conditional-dependence measures based on Spearman’s rho is introduced. The corresponding multidimensional versions are established. Asymptotic distributional results are derived for related estimators which are based on the empirical copula. Particular emphasis is placed on a new type of multidimensional tail-dependence measure and its relationship to other measures of tail dependence is shown. Multivariate tail dependence describes the limiting amount of dependence in the vertices of the copula’s domain.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E20 Asymptotic distribution theory in statistics
62H20 Measures of association (correlation, canonical correlation, etc.)
60F05 Central limit and other weak theorems
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