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, exploring their theoretical foundations and connections to halfspace depth, with implications for statistical analysis of multivariate data.

Contribution

It provides a comprehensive discussion linking multivariate quantiles, $L_1$ optimization, and halfspace depth, clarifying their relationships and theoretical properties.

Findings

Elucidates the connection between multivariate quantiles and halfspace depth.

Highlights the role of $L_1$ optimization in defining multivariate quantiles.

Provides insights into the theoretical properties of multivariate 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]