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

By Friedrich Schmid, Rafael Schmidt. 2007

109 citations recorded by the source corpus.

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.

Subfields: Finance, Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4b831916c9eb565e0f257018674d6970b0e5c41d

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In Finance

In Global and Planetary Change

In Statistics and Probability

Citations in the corpus

Copula-based Measurement of Dependence Between Dimensions of Well-being (2014, background): “(X) is the mean of two multidimensional rank correlation coe¢ cients discussed in Joe (1990) and has been studied by Nelsen (1991, 2002), Dolati and Úbeda-Flores (2006), Schmid and Schmidt (2006, 2007) and Taylor (2007).”
Copula-Based Measures of Multivariate Association (2010, methodology): “Schmid and Schmidt [93] studied more general extensions of Blomqvist’s beta,”
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].”
Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence (2007, methodology): “Various multivariate versions of Spearman’s ρ are e.g. discussed in Wolff (1980), Joe (1990), Nelsen (1996), and Schmid and Schmidt (2006a).”
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. ”
Multivariate Extensions of Spearman's Rho and Related Statistics (2007, methodology): “An empirical analysis of this bootstrap procedure is presented in Schmid and Schmidt (2006) and its applicability in the context of measuring price comovements in financial markets is discussed in Penzer et al. (2006).”