Discussion of: Brownian distance covariance

Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]Comment: Published in at http://dx.doi.org/10.1214/09-AOAS312G the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical Inference using the Morse-Smale Complex

The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare multivariate functions. In this paper, we present some statistical results on estimating Morse-Smale complexes. This allows us to derive new results for two existing methods: mode clustering and Morse-Smale regression. We also develop two new methods based on the Morse-Smale complex: a visualization technique for multivariate functions and a two-sample, multivariate hypothesis test.Comment: 45 pages, 13 figures. Accepted to Electronic Journal of Statistic