Multivariate conditional versions of Spearmanʹs rho and related measures of tail dependence

A new family of conditional-dependence measures based on Spearmanʹs 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 copulaʹs domain.