Multiple-output composite quantile regression through an optimal transport lens

Yang, Xuzhi and Wang, Tengyao ORCID: 0000-0003-2072-6645 (2024) Multiple-output composite quantile regression through an optimal transport lens. Proceedings of Machine Learning Research, 247. pp. 5076-5122. ISSN 2640-3498

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Abstract

Composite quantile regression has been used to obtain robust estimators of regression coefficients in linear models with good statistical efficiency. By revealing an intrinsic link between the composite quantile regression loss function and the Wasserstein distance from the residuals to the set of quantiles, we establish a generalization of the composite quantile regression to the multiple-output settings. Theoretical convergence rates of the proposed estimator are derived both under the setting where the additive error possesses only a finite ℓ-th moment (for ℓ > 2) and where it exhibits a sub-Weibull tail. In doing so, we develop novel techniques for analyzing the M-estimation problem that involves Wasserstein-distance in the loss. Numerical studies confirm the practical effectiveness of our proposed procedure.

Item Type:	Article
Additional Information:	© 2024 The Author(s)
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science H Social Sciences > HA Statistics
Date Deposited:	01 Oct 2024 16:06
Last Modified:	20 Nov 2024 16:21
URI:	http://eprints.lse.ac.uk/id/eprint/125589

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