Rejoinder to "Multivariate quantiles and multiple-output regression quantiles: From $L_1$ optimization to halfspace depth"
Marc Hallin, Davy Paindaveine, Miroslav \v{S}iman
TL;DR
This paper provides a response to prior work on multivariate quantiles and multiple-output regression quantiles, discussing the theoretical foundations and implications of these statistical concepts.
Contribution
It offers a critical analysis and clarification of the relationships between $L_1$ optimization, halfspace depth, and multivariate quantiles.
Findings
Clarifies the connection between $L_1$ optimization and halfspace depth
Highlights the theoretical implications for multivariate quantiles
Addresses misconceptions in previous literature
Abstract
Rejoinder to "Multivariate quantiles and multiple-output regression quantiles: From optimization to halfspace depth" by M. Hallin, D. Paindaveine and M. Siman [arXiv:1002.4486]
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