IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v149y2016icp1-12.html

Statistical consistency of coefficient-based conditional quantile regression

Author

Listed:
  • Cai, Jia
  • Xiang, Dao-Hong

Abstract

This study focuses on the coefficient-based conditional quantile regression associated with lq-regularization term, where 1≤q≤2. Error analysis is investigated based on the capacity of the hypothesis space. The linear piecewise nature of the pinball loss function for quantile regression and the lq-penalty of the learning algorithm lead to some difficulties in the theoretical analysis. In order to overcome the difficulties, we introduce a novel error decomposition formula. The prolix iteration is then circumvented in the error analysis. Some satisfactory learning rates are achieved in a general setting under mild conditions.

Suggested Citation

  • Cai, Jia & Xiang, Dao-Hong, 2016. "Statistical consistency of coefficient-based conditional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 1-12.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:1-12
    DOI: 10.1016/j.jmva.2016.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16300021
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.03.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    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. Yu, Dengdeng & Zhang, Li & Mizera, Ivan & Jiang, Bei & Kong, Linglong, 2019. "Sparse wavelet estimation in quantile regression with multiple functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 12-29.
    2. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
    3. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    4. Chen, Bingzhen & Zhai, Wenjuan, 2025. "Unified algorithms for distributed regularized linear regression model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 867-884.
    5. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    6. Torossian, Léonard & Picheny, Victor & Faivre, Robert & Garivier, Aurélien, 2020. "A review on quantile regression for stochastic computer experiments," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    7. Park, Jinho, 2017. "Solution path for quantile regression with epsilon-insensitive loss in a reproducing kernel Hilbert space," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 205-211.
    8. Christophe Crambes & Ali Gannoun & Yousri Henchiri, 2014. "Modelling functional additive quantile regression using support vector machines approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 639-668, December.
    9. Park, Jinho & Kim, Jeankyung, 2011. "Quantile regression with an epsilon-insensitive loss in a reproducing kernel Hilbert space," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 62-70, January.
    10. Stromberg, Per M. & Öhrner, Erik & Brockwell, Erik & Liu, Zhaoyang, 2021. "Valuing urban green amenities with an inequality lens," Ecological Economics, Elsevier, vol. 186(C).
    11. Tian, Yuzhu & Song, Xinyuan, 2020. "Bayesian bridge-randomized penalized quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    12. Zou, Hui & Yuan, Ming, 2008. "Regularized simultaneous model selection in multiple quantiles regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5296-5304, August.
    13. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.
    14. Naoto Jinji & Xingyuan Zhang & Shoji Haruna, 2022. "Does Tobin’s q Matter for a Firm’s Choice of Globalization Mode?," Advances in Japanese Business and Economics, in: Deep Integration, Global Firms, and Technology Spillovers, chapter 0, pages 49-69, Springer.
    15. Guangrui Tang & Neng Fan, 2022. "A Survey of Solution Path Algorithms for Regression and Classification Models," Annals of Data Science, Springer, vol. 9(4), pages 749-789, August.
    16. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
    17. Alexander Aue & Rex C. Y. Cheung & Thomas C. M. Lee & Ming Zhong, 2014. "Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1241-1256, September.
    18. Crambes, Christophe & Gannoun, Ali & Henchiri, Yousri, 2011. "Weak consistency of the Support Vector Machine Quantile Regression approach when covariates are functions," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1847-1858.
    19. Songfeng Zheng, 2014. "A generalized Newton algorithm for quantile regression models," Computational Statistics, Springer, vol. 29(6), pages 1403-1426, December.
    20. Shu, Lei & Hao, Yifan & Chen, Yu & Yang, Qing, 2025. "SFQRA: Scaled factor-augmented quantile regression with aggregation in conditional mean forecasting," Journal of Multivariate Analysis, Elsevier, vol. 207(C).

    More about this item

    Keywords

    ;
    ;
    ;

    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:eee:jmvana:v:149:y:2016:i:c:p:1-12. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.