Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence

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A multivariate version of Hoeffding's Phi-Square (2010, methodology): “…measure of association Copula Nonparametric estimation Empirical copula process Weak convergence Nonparametric bootstrap Strong mixing a b s t r a c t A multivariate measure of association is proposed, which extends the bivariate copulabased measure Phi-Square introduced by Hoeffding [22].”
Properties of hierarchical Archimedean copulas (2013, methodology): “The representation of the copula in terms of the Laplace transforms is very useful for simulation purposes (see Whelan (2004), McNeil (2008), Hofert (2008), Marshall and Olkin (1988)).”
Tail dependence functions and vine copulas (2010, methodology): “where C denotes the survival function of C. Bivariate tail dependence has been widely studied (Joe, 1997), and various multivariate versions of tail dependence parameters have also been introduced and studied in Schmidt (2002), Frahm (2006), Schmid and Schmidt (2007a, 2007b) , Kl uppelberg et al. ”
Copula-Based Measures of Multivariate Association (2010, methodology): “Schmid and Schmidt [93, 95] define multivariate generalizations of λL which are based on conditional versions of Spearman’s rho and Blomqvist’s beta.”