Prof. Gabor J. Szekely : Measuring and Testing Dependence by Correlation of Distances

Posted by , part of the Statistics and Data Science Seminar.

At

March 21, 2007, 3:30 p.m.

In

SEO 712

Abstract

We introduce a simple new measure of dependence between random vectors. Distance covariance (dCov) and distance correlation (dCor) are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, dCor = 0 characterizes independence for the general case. The empirical dCov and dCor are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Definitions can be extended to metric-space-valued observations where the random vectors could even be in different metric spaces. Asymptotic properties and applications in testing independence will also be discussed. A new universally consistent test of multivariate independence is developed. Implementation of the test and Monte Carlo results are presented.