IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i12p1847-1858.html
   My bibliography  Save this article

Weak consistency of the Support Vector Machine Quantile Regression approach when covariates are functions

Author

Listed:
  • Crambes, Christophe
  • Gannoun, Ali
  • Henchiri, Yousri

Abstract

This paper deals with a nonparametric estimation of conditional quantile regression when the explanatory variable X takes its values in a bounded subspace of a functional space X and the response Y takes its values in a compact of the space Y≔R. The functional observations, X1,…,Xn, are projected onto a finite dimensional subspace having a suitable orthonormal system. The Xi’s will be characterized by their coordinates in this basis. We perform the Support Vector Machine Quantile Regression approach in finite dimension with the selected coefficients. Then we establish weak consistency of this estimator. The various parameters needed for the construction of this estimator are automatically selected by data-splitting and by penalized empirical risk minimization.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1847-1858
    DOI: 10.1016/j.spl.2011.07.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211002392
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2011.07.008?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. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    2. 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.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Crambes, Christophe & Gannoun, Ali & Henchiri, Yousri, 2013. "Support vector machine quantile regression approach for functional data: Simulation and application studies," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 50-68.
    3. 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.

    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. 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.
    3. 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.
    4. 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.
    5. He, Yaoyao & Zheng, Yaya, 2018. "Short-term power load probability density forecasting based on Yeo-Johnson transformation quantile regression and Gaussian kernel function," Energy, Elsevier, vol. 154(C), pages 143-156.
    6. Crambes, Christophe & Gannoun, Ali & Henchiri, Yousri, 2013. "Support vector machine quantile regression approach for functional data: Simulation and application studies," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 50-68.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Songfeng Zheng, 2014. "A generalized Newton algorithm for quantile regression models," Computational Statistics, Springer, vol. 29(6), pages 1403-1426, December.
    12. Y. Andriyana & I. Gijbels & A. Verhasselt, 2014. "P-splines quantile regression estimation in varying coefficient models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 153-194, March.
    13. He, Yaoyao & Liu, Rui & Li, Haiyan & Wang, Shuo & Lu, Xiaofen, 2017. "Short-term power load probability density forecasting method using kernel-based support vector quantile regression and Copula theory," Applied Energy, Elsevier, vol. 185(P1), pages 254-266.
    14. Yufeng Liu & Yichao Wu, 2011. "Simultaneous multiple non-crossing quantile regression estimation using kernel constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 415-437.
    15. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    16. Muller, Christophe, 2018. "Heterogeneity and nonconstant effect in two-stage quantile regression," Econometrics and Statistics, Elsevier, vol. 8(C), pages 3-12.
    17. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    18. Narisetty, Naveen & Koenker, Roger, 2022. "Censored quantile regression survival models with a cure proportion," Journal of Econometrics, Elsevier, vol. 226(1), pages 192-203.
    19. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    20. 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.

    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:stapro:v:81:y:2011:i:12:p:1847-1858. 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.