Multivariate conditional versions of Spearman's rho and related measures of tail dependence

Authors:
Friedrich Schmid;Rafael Schmidt
Affiliations:
Seminar für Wirtschafts- und Sozialstatistik, Universität zu Köln, Albertus-Magnus-Platz, D-50923 Köln, Germany;Seminar für Wirtschafts- und Sozialstatistik, Universität zu Köln, Albertus-Magnus-Platz, D-50923 Köln, Germany
Venue:
Journal of Multivariate Analysis
Year:
2007

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Abstract

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.