IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/125589.html
   My bibliography  Save this paper

Multiple-output composite quantile regression through an optimal transport lens

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/125589/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:spo:wpmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
    2. 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.
    3. Marc Hallin & Daniel Hlubinka & Šárka Hudecová, 2023. "Efficient Fully Distribution-Free Center-Outward Rank Tests for Multiple-Output Regression and MANOVA," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1923-1939, July.
    4. 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.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. 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.
    7. repec:hal:spmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
    8. 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.
    9. Jianqing Fan & Quefeng Li & Yuyan Wang, 2017. "Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 247-265, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Han, Dongxiao & Huang, Jian & Lin, Yuanyuan & Shen, Guohao, 2022. "Robust post-selection inference of high-dimensional mean regression with heavy-tailed asymmetric or heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 230(2), pages 416-431.
    2. Man, Rebeka & Tan, Kean Ming & Wang, Zian & Zhou, Wen-Xin, 2024. "Retire: Robust expectile regression in high dimensions," Journal of Econometrics, Elsevier, vol. 239(2).
    3. Luo, Jiyu & Sun, Qiang & Zhou, Wen-Xin, 2022. "Distributed adaptive Huber regression," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    4. Chen, Huangyue & Kong, Lingchen & Shang, Pan & Pan, Shanshan, 2020. "Safe feature screening rules for the regularized Huber regression," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    5. Dongxiao Han & Miao Han & Jian Huang & Yuanyuan Lin, 2023. "Robust inference for high‐dimensional single index models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1590-1615, December.
    6. Yuyang Liu & Pengfei Pi & Shan Luo, 2023. "A semi-parametric approach to feature selection in high-dimensional linear regression models," Computational Statistics, Springer, vol. 38(2), pages 979-1000, June.
    7. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    8. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    9. Jiang, Rong & Qian, Weimin & Zhou, Zhangong, 2012. "Variable selection and coefficient estimation via composite quantile regression with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 308-317.
    10. Fan, Jianqing & Guo, Yongyi & Jiang, Bai, 2022. "Adaptive Huber regression on Markov-dependent data," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 802-818.
    11. Chen, Zhao & Cheng, Vivian Xinyi & Liu, Xu, 2024. "Reprint: Hypothesis testing on high dimensional quantile regression," Journal of Econometrics, Elsevier, vol. 239(2).
    12. Sulkhan Chavleishvili & Simone Manganelli, 2024. "Forecasting and stress testing with quantile vector autoregression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 66-85, January.
    13. Xiao, Xuan & Xu, Xingbai & Zhong, Wei, 2023. "Huber estimation for the network autoregressive model," Statistics & Probability Letters, Elsevier, vol. 203(C).
    14. Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.
    15. Song, Yunquan & Liang, Xijun & Zhu, Yanji & Lin, Lu, 2021. "Robust variable selection with exponential squared loss for the spatial autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    16. Wang, Chuchu & Song, Xinyuan, 2024. "Nonparametric quantile scalar-on-image regression," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    17. Kean Ming Tan & Lan Wang & Wen‐Xin Zhou, 2022. "High‐dimensional quantile regression: Convolution smoothing and concave regularization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 205-233, February.
    18. Neil Shephard, 2020. "An estimator for predictive regression: reliable inference for financial economics," Papers 2008.06130, arXiv.org.
    19. Jianqing Fan & Donggyu Kim & Minseok Shin & Yazhen Wang, 2024. "Factor and Idiosyncratic VAR-Ito Volatility Models for Heavy-Tailed High-Frequency Financial Data," Working Papers 202415, University of California at Riverside, Department of Economics.
    20. Yang, Shuquan & Ling, Nengxiang, 2023. "Robust projected principal component analysis for large-dimensional semiparametric factor modeling," Journal of Multivariate Analysis, Elsevier, vol. 195(C).

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:125589. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.