Discussion of: Brownian distance covariance

TL;DR

This paper discusses the concept of Brownian distance covariance, its potential extensions for high-dimensional data and increased power, highlighting its significance in dependency evaluation in statistics.

Contribution

It introduces two extensions of Brownian distance covariance, expanding its applicability to high-dimensional data and improving its statistical power.

Findings

Potential for high-dimensional data analysis

Extensions may increase statistical power

Significance in dependency evaluation

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]