IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v149y2016icp1-12.html
   My bibliography  Save this article

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 search 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, January.
    3. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    4. 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. 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).
    3. 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).
    4. Tian, Yuzhu & Song, Xinyuan, 2020. "Bayesian bridge-randomized penalized quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. 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.
    6. 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.
    7. Araujo, Gustavo Silva & Gaglianone, Wagner Piazza, 2023. "Machine learning methods for inflation forecasting in Brazil: New contenders versus classical models," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 4(2).
    8. Yichao Wu, 2011. "An ordinary differential equation-based solution path algorithm," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 185-199.
    9. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    10. Oxana Babecka Kucharcukova & Jan Bruha, 2016. "Nowcasting the Czech Trade Balance," Working Papers 2016/11, Czech National Bank.
    11. Carstensen, Kai & Heinrich, Markus & Reif, Magnus & Wolters, Maik H., 2020. "Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 829-850.
    12. Hou-Tai Chang & Ping-Huai Wang & Wei-Fang Chen & Chen-Ju Lin, 2022. "Risk Assessment of Early Lung Cancer with LDCT and Health Examinations," IJERPH, MDPI, vol. 19(8), pages 1-12, April.
    13. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    14. Nicolaj N. Mühlbach, 2020. "Tree-based Synthetic Control Methods: Consequences of moving the US Embassy," CREATES Research Papers 2020-04, Department of Economics and Business Economics, Aarhus University.
    15. Wang, Qiao & Zhou, Wei & Cheng, Yonggang & Ma, Gang & Chang, Xiaolin & Miao, Yu & Chen, E, 2018. "Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 120-145.
    16. Dmitriy Drusvyatskiy & Adrian S. Lewis, 2018. "Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 919-948, August.
    17. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    18. Lucian Belascu & Alexandra Horobet & Georgiana Vrinceanu & Consuela Popescu, 2021. "Performance Dissimilarities in European Union Manufacturing: The Effect of Ownership and Technological Intensity," Sustainability, MDPI, vol. 13(18), pages 1-19, September.
    19. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    20. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.

    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.