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Robust functional linear regression based on splines

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  • Maronna, Ricardo A.
  • Yohai, Victor J.

Abstract

Many existing methods for functional regression are based on the minimization of an L2 norm of the residuals and are therefore sensitive to atypical observations, which may affect the predictive power and/or the smoothness of the resulting estimate. A robust version of a spline-based estimate is presented, which has the form of an MM estimate, where the L2 loss is replaced by a bounded loss function. The estimate can be computed by a fast iterative algorithm. The proposed approach is compared, with favorable results, to the one based on L2 and to both classical and robust Partial Least Squares through an example with high-dimensional real data and a simulation study.11Matlab code for the proposed procedure is provided as supplemental material.

Suggested Citation

  • Maronna, Ricardo A. & Yohai, Victor J., 2013. "Robust functional linear regression based on splines," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 46-55.
    • Handle: RePEc:eee:csdana:v:65:y:2013:i:c:p:46-55
    DOI: 10.1016/j.csda.2011.11.014
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    References listed on IDEAS

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    1. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2012. "Functional linear regression after spline transformation," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 587-601.
    2. Cardot, Herve & Crambes, Christophe & Kneip, Alois & Sarda, Pascal, 2007. "Smoothing splines estimators in functional linear regression with errors-in-variables," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4832-4848, June.
    3. C. Crambes & L. Delsol & A. Laksaci, 2008. "Robust nonparametric estimation for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 573-598.
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    Cited by:

    1. Peter Hall & Giles Hooker, 2016. "Truncated linear models for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 637-653, June.
    2. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    3. Kalogridis, Ioannis & Van Aelst, Stefan, 2019. "Robust functional regression based on principal components," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 393-415.
    4. Kalogridis, Ioannis & Van Aelst, Stefan, 2023. "Robust penalized estimators for functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    5. Italo R. Lima & Guanqun Cao & Nedret Billor, 2019. "Robust simultaneous inference for the mean function of functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 785-803, September.
    6. Boente, Graciela & Parada, Daniela, 2023. "Robust estimation for functional quadratic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    7. Guodong Shan & Yiheng Hou & Baisen Liu, 2020. "Bayesian robust estimation of partially functional linear regression models using heavy-tailed distributions," Computational Statistics, Springer, vol. 35(4), pages 2077-2092, December.
    8. Boente, Graciela & Salibian-Barrera, Matías & Vena, Pablo, 2020. "Robust estimation for semi-functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    9. Italo R. Lima & Guanqun Cao & Nedret Billor, 2019. "M-based simultaneous inference for the mean function of functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 577-598, June.
    10. Martínez-Hernández, Israel & Genton, Marc G. & González-Farías, Graciela, 2019. "Robust depth-based estimation of the functional autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 66-79.

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