Directional Dependence in Multivariate Distributions

DATE: November 12, 2009

TIME: 11:00 AM – 12:00 PM

LOCATION: Executive classroom

FEES: none

EVENT CONTACT:

Nagi Gebraeel, ISyE
Contact Nagi Gebraeel
404-894-0054

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 associationâ€"-such as the population versions of Spearman’s rho and Kendall’s tauâ€"-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.