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Robust nonparametric estimation for functional data

Author

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  • C. Crambes
  • L. Delsol
  • A. Laksaci

Abstract

Robust estimation provides an alternative approach to classical methods, for instance, when the data are affected by the presence of outliers. Recently, these robust estimators have been considered for models with functional data. In this paper, we focus on asymptotic properties of a conditional nonparametric estimation of a real-valued variable with a functional covariate. We present results dealing with 𝕃q errors of these estimators. Then, our estimation procedure is evaluated by means of some applications to real data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:573-598
    DOI: 10.1080/10485250802331524
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    Citations

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    Cited by:

    1. Saliha Derrar & Ali Laksaci & Elias Ould Saïd, 2020. "M-estimation of the regression function under random left truncation and functional time series model," Statistical Papers, Springer, vol. 61(3), pages 1181-1202, June.
    2. Boente, Graciela & Vahnovan, Alejandra, 2015. "Strong convergence of robust equivariant nonparametric functional regression estimators," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 1-11.
    3. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2012. "Functional linear regression after spline transformation," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 587-601.
    4. 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.
    5. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    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. Joseph Ngatchou-Wandji & Marwa Ltaifa & Didier Alain Njamen Njomen & Jia Shen, 2022. "Nonparametric Estimation of the Density Function of the Distribution of the Noise in CHARN Models," Mathematics, MDPI, vol. 10(4), pages 1-20, February.
    8. Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
    9. Demongeot, Jacques & Hamie, Ali & Laksaci, Ali & Rachdi, Mustapha, 2016. "Relative-error prediction in nonparametric functional statistics: Theory and practice," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 261-268.
    10. Bouzebda, Salim & Chaouch, Mohamed, 2022. "Uniform limit theorems for a class of conditional Z-estimators when covariates are functions," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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