Statistics and Data Science Seminar
Prof. Gabor J. Szekely
National Science Foundation
Measuring and Testing Dependence by Correlation of Distances
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.
Wednesday March 21, 2007 at 3:30 PM in SEO 712