We discuss briefly the very interesting concept of Brownian distance covariance developed by Székely 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 Székely 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.
"Discussion of: Brownian distance covariance." Ann. Appl. Stat. 3 (4) 1270 - 1278, December 2009. https://doi.org/10.1214/09-AOAS312B