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Support vector machine quantile regression approach for functional data: Simulation and application studies

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

Abstract

The topic of this paper is related to quantile regression when the covariate is a function. The estimator we are interested in, based on the Support Vector Machine method, was introduced in Crambes et al. (2011) [11]. We improve the results obtained in this former paper, giving a rate of convergence in probability of the estimator. In addition, we give a practical method to construct the estimator, solution of a penalized L1-type minimization problem, using an Iterative Reweighted Least Squares procedure. We evaluate the performance of the estimator in practice through simulations and a real data set study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:121:y:2013:i:c:p:50-68
    DOI: 10.1016/j.jmva.2013.06.004
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    10. 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.
    11. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
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    Cited by:

    1. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2023. "Functional Data Inference in a Parametric Quantile Model applied to Lifetime Income Curves," Working papers 2023rwp-211, Yonsei University, Yonsei Economics Research Institute.
    2. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    4. Jin Seo Cho & Meng Huang & Halbert White, 2021. "Testing a Constant Mean Function Using Functional Regression," Working papers 2021rwp-190, Yonsei University, Yonsei Economics Research Institute.
    5. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    6. 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.

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