Department of
presents
Gabor J. Szekely
Program Director, NSF, Division of Mathematical Sciences
Brownian Covariance: 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. It turnes out that dCov can easily
be understood and defined via Brownian motions, in this way we can define the
Brownian covariance, a natural and effective counterpart of Pearson's classical
covariance.
Friday, October 26, 2007
3:35 - 4:15 pm
301 Riddick Hall
Refreshments will be served in the common area of 301 Riddick at 3:00 pm.