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Multiple-output composite quantile regression through an optimal transport lens

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  • Yang, Xuzhi
  • Wang, Tengyao

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.

Suggested Citation

  • Yang, Xuzhi & Wang, Tengyao, 2024. "Multiple-output composite quantile regression through an optimal transport lens," LSE Research Online Documents on Economics 125589, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:125589
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    File URL: http://eprints.lse.ac.uk/125589/
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    References listed on IDEAS

    as
    1. Eustasio del Barrio & Alberto González-Sanz & Marc Hallin, 2022. "Nonparametric Multiple-Output Center-Outward Quantile Regression," Working Papers ECARES 2022-10, ULB -- Universite Libre de Bruxelles.
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    3. Lan Wang & Bo Peng & Runze Li, 2015. "A High-Dimensional Nonparametric Multivariate Test for Mean Vector," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1658-1669, December.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July.
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    7. Qiang Sun & Wen-Xin Zhou & Jianqing Fan, 2020. "Adaptive Huber Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 254-265, January.
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    More about this item

    Keywords

    multivariate quantiles; optimal transport; quantile regression; robust estimation;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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