Multiple-output composite quantile regression through an optimal transport lens

Xuzhi Yang and Tengyao Wang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: multivariate quantiles; optimal transport; quantile regression; robust estimation (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2024-06-30
New Economics Papers: this item is included in nep-ecm
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Published in Proceedings of Machine Learning Research, 30, June, 2024, 247, pp. 5076-5122. ISSN: 2640-3498

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