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On the local linear modelization of the conditional density for functional and ergodic data

Author

Listed:
  • Somia Ayad

    (Université Docteur Moulay Taher)

  • Ali Laksaci

    (King Khalid University)

  • Saâdia Rahmani

    (Université Docteur Moulay Taher)

  • Rachida Rouane

    (Université Docteur Moulay Taher)

Abstract

In this paper, we estimate the conditional density function using the local linear approach. We treat the case when the regressor is valued in a semi-metric space, the response is a scalar and the data are observed as ergodic functional times series. Under this dependence structure, we state the almost complete consistency (a.co.) with rates of the constructed estimator. Moreover, the usefulness of our results is illustrated through their application to the conditional mode estimation.

Suggested Citation

  • Somia Ayad & Ali Laksaci & Saâdia Rahmani & Rachida Rouane, 2020. "On the local linear modelization of the conditional density for functional and ergodic data," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 237-254, August.
    • Handle: RePEc:spr:metron:v:78:y:2020:i:2:d:10.1007_s40300-020-00174-6
    DOI: 10.1007/s40300-020-00174-6
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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. Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
    3. 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.
    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.
    5. 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.
    6. Sophie Dabo-Niang & Ali Laksaci, 2010. "Note on conditional mode estimation for functional dependent data," Statistica, Department of Statistics, University of Bologna, vol. 70(1), pages 83-94.
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    Cited by:

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