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Functional data analysis: local linear estimation of the $$L_1$$ L 1 -conditional quantiles

Author

Listed:
  • Fahimah A. Al-Awadhi

    (Kuwait University)

  • Zoulikha Kaid

    (King Khalid University)

  • Ali Laksaci

    (King Khalid University)

  • Idir Ouassou

    (Université Cadi Ayyad
    University Mohammed VI Polytechnique)

  • Mustapha Rachdi

    (University Grenoble Alpes)

Abstract

We consider a new estimator of the quantile function of a scalar response variable given a functional random variable. This new estimator is based on the $$L_1$$ L 1 approach. Under standard assumptions, we prove the almost-complete consistency as well as the asymptotic normality of this estimator. This new approach is also illustrated through some simulated data and its superiority, compared to the classical method, has been proved for practical purposes.

Suggested Citation

  • Fahimah A. Al-Awadhi & Zoulikha Kaid & Ali Laksaci & Idir Ouassou & Mustapha Rachdi, 2019. "Functional data analysis: local linear estimation of the $$L_1$$ L 1 -conditional quantiles," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 217-240, June.
    • Handle: RePEc:spr:stmapp:v:28:y:2019:i:2:d:10.1007_s10260-018-00447-5
    DOI: 10.1007/s10260-018-00447-5
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    References listed on IDEAS

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    1. Runtong Zhang & Zhenji Zhang & Kecheng Liu & Juliang Zhang (ed.), 2015. "Liss 2013," Springer Books, Springer, number 978-3-642-40660-7, January.
    2. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    3. 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.
    4. Kangning Wang & Lu Lin, 2015. "Variable Selection in Semiparametric Quantile Modeling for Longitudinal Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(11), pages 2243-2266, June.
    5. Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    6. Sophie Dabo-Niang & Zoulikha Kaid & Ali Laksaci, 2015. "Asymptotic properties of the kernel estimate of spatial conditional mode when the regressor is functional," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 131-160, April.
    7. Racine, Jeffrey S. & Li, Kevin, 2017. "Nonparametric conditional quantile estimation: A locally weighted quantile kernel approach," Journal of Econometrics, Elsevier, vol. 201(1), pages 72-94.
    8. Laksaci, Ali & Lemdani, Mohamed & Ould-Sad, Elias, 2009. "A generalized L1-approach for a kernel estimator of conditional quantile with functional regressors: Consistency and asymptotic normality," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1065-1073, April.
    9. Ying Lu & Jiang Du & Zhimeng Sun, 2014. "Functional partially linear quantile regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 317-332, February.
    10. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(5), pages 793-813, December.
    11. Fatiha Messaci & Nahima Nemouchi & Idir Ouassou & Mustapha Rachdi, 2015. "Local polynomial modelling of the conditional quantile for functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 597-622, November.
    12. Zhenji Zhang & Zuojun Max Shen & Juliang Zhang & Runtong Zhang (ed.), 2015. "Liss 2014," Springer Books, Springer, edition 127, number 978-3-662-43871-8, January.
    13. Samanta, M., 1989. "Non-parametric estimation of conditional quantiles," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 407-412, April.
    14. Demongeot, Jacques & Naceri, Amina & Laksaci, Ali & Rachdi, Mustapha, 2017. "Local linear regression modelization when all variables are curves," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 37-44.
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    Cited by:

    1. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    2. 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).
    3. Litimein, Ouahiba & Laksaci, Ali & Ait-Hennani, Larbi & Mechab, Boubaker & Rachdi, Mustapha, 2024. "Asymptotic normality of the local linear estimator of the functional expectile regression," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    4. Ali Laksaci & Elias Ould Saïd & Mustapha Rachdi, 2021. "Uniform consistency in number of neighbors of the kNN estimator of the conditional quantile model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 895-911, August.
    5. Ibrahim M. Almanjahie & Salim Bouzebda & Zoulikha Kaid & Ali Laksaci, 2024. "The local linear functional kNN estimator of the conditional expectile: uniform consistency in number of neighbors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(8), pages 1007-1035, November.
    6. Amel, Azzi & Ali, Laksaci & Elias, Ould Saïd, 2022. "On the robustification of the kernel estimator of the functional modal regression," Statistics & Probability Letters, Elsevier, vol. 181(C).
    7. Saâdia Rahmani & Oussama Bouanani, 2023. "Local linear estimation of the conditional cumulative distribution function: Censored functional data case," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 741-769, February.

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