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Local linear estimate of the nonparametric robust regression in functional data

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  • Belarbi, Faiza
  • Chemikh, Souheyla
  • Laksaci, Ali

Abstract

In this paper, we study the robust estimation of the functional local linear regression model. The main results of this work are the establishment of the almost complete convergence as well as the asymptotic normality for the constructed estimator.

Suggested Citation

  • Belarbi, Faiza & Chemikh, Souheyla & Laksaci, Ali, 2018. "Local linear estimate of the nonparametric robust regression in functional data," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 128-133.
    • Handle: RePEc:eee:stapro:v:134:y:2018:i:c:p:128-133
    DOI: 10.1016/j.spl.2017.11.003
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    References listed on IDEAS

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    1. J. Barrientos-Marin & F. Ferraty & P. Vieu, 2010. "Locally modelled regression and functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 617-632.
    2. Zhiyong Zhou & Zhengyan Lin, 2016. "Asymptotic normality of locally modelled regression estimator for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 116-131, March.
    3. Kara, Lydia-Zaitri & Laksaci, Ali & Rachdi, Mustapha & Vieu, Philippe, 2017. "Data-driven kNN estimation in nonparametric functional data analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 176-188.
    4. Lydia Kara-Zaitri & Ali Laksaci & Mustapha Rachdi & Philippe Vieu, 2017. "Uniform in bandwidth consistency for various kernel estimators involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 85-107, January.
    5. Boente, Graciela & Vahnovan, Alejandra, 2015. "Strong convergence of robust equivariant nonparametric functional regression estimators," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 1-11.
    6. A. Berlinet & A. Elamine & A. Mas, 2011. "Local linear regression for functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1047-1075, October.
    7. Cai, Zongwu & Ould-Saïd, Elias, 2003. "Local M-estimator for nonparametric time series," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 433-449, December.
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