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Modelling functional additive quantile regression using support vector machines approach

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  • Christophe Crambes
  • Ali Gannoun
  • Yousri Henchiri

Abstract

This work deals with conditional quantiles estimation when several functional covariates are involved, via a support vector machines nonparametric methodology. We establish weak consistency of this estimator. To fit the additive components, we use an ordinary backfitting procedure combined with an iterative reweighted least-squares procedure to solve the penalised minimisation problem. This procedure makes it possible to derive a split sample method for choosing the hyper-parameters of the model. The performances of the proposed technique, in terms of forecast accuracy, are evaluated through simulation and a real dataset study.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:639-668
    DOI: 10.1080/10485252.2014.941365
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    References listed on IDEAS

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    1. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    2. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November.
    3. De Gooijer, Jan G. & Gannoun, Ali & Zerom, Dawit, 2002. "Mean squared error properties of the kernel-based multi-stage median predictor for time series," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 51-56, January.
    4. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
    5. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    6. Christmann, Andreas & Hable, Robert, 2012. "Consistency of support vector machines using additive kernels for additive models," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 854-873.
    7. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    8. Anderson-Cook, Christine M., 2008. "Modern Experimental Design. Thomas P. Ryan," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 426-427, March.
    9. 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.
    10. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    11. 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.
    12. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    13. Doksum, Kjell & Koo, Ja-Yong, 2000. "On spline estimators and prediction intervals in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 35(1), pages 67-82, November.
    14. 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.
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