Discussion of: Brownian distance covariance

Abstract

We discuss briefly the very interesting concept of Brownian distance covariance developed by Sz\'{e}kely and Rizzo [Ann. Appl. Statist. (2009), to appear] and describe two possible extensions. The first extension is for high dimensional data that can be coerced into a Hilbert space, including certain high throughput screening and functional data settings. The second extension involves very simple modifications that may yield increased power in some settings. We commend Sz\'{e}kely and Rizzo for their very interesting work and recognize that this general idea has potential to have a large impact on the way in which statisticians evaluate dependency in data. [arXiv:1010.0297]Comment: Published in at http://dx.doi.org/10.1214/09-AOAS312B the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org). With Correction