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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. 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.
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    4. 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.
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    Citations

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    Cited by:

    1. 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).
    2. 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.
    3. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(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. 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).
    6. 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).

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