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TITLE: Directional Dependence in Multivariate Distributions
SPEAKER: Roger Nelsen
ABSTRACT:
One of the simplest ways of measuring dependence in statistics is via a measure of association. Scale-invariant or distribution-free measures of association—-such as the population versions of Spearman’s rho and Kendall’s tau—-are well understood in the bivariate case, but much less well known in the multivariate case. In both the bivariate and multivariate cases, such measures are functions of the copula of the random variables, the function that joins or couples a multivariate distribution function to its one-dimensional marginal distribution functions.
Several multivariate extensions of Spearman’s rho have been proposed. But they can fail to detect dependence in some multivariate distributions. In this talk we will propose several “coefficients of dependence” to remedy this situation (in the trivariate case) and study their properties. We also examine similar results for Kendall’s tau and Blomqvist’s beta.
