Discussion of "Multivariate quantiles and multiple-output regression quantiles: From $L_1$ optimization to halfspace depth"

TL;DR

This paper discusses the concepts of multivariate quantiles and multiple-output regression quantiles, connecting $L_1$ optimization methods to the geometric notion of halfspace depth, providing insights into their theoretical foundations.

Contribution

It offers a comprehensive discussion linking $L_1$ optimization techniques with halfspace depth in the context of multivariate quantiles and regression quantiles.

Findings

Clarifies the relationship between $L_1$ optimization and halfspace depth

Highlights the theoretical properties of multivariate quantiles

Provides insights into the geometric interpretation of regression quantiles

Abstract

Discussion of "Multivariate quantiles and multiple-output regression quantiles: From $L_1$ optimization to halfspace depth" by M. Hallin, D. Paindaveine and M. Siman [arXiv:1002.4486]