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FDA: strong consistency of the NN local linear estimation of the functional conditional density and mode

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  • Zouaoui Chikr-Elmezouar
  • Ibrahim M. Almanjahie
  • Ali Laksaci
  • Mustapha Rachdi

Abstract

In this paper we present a new estimator of the conditional density and mode when the co-variables are of functional kind. This estimator is a combination of both, the k-Nearest Neighbours procedure and the functional local linear estimation. Then, for each statistical parameter (conditional density or mode), results concerning the strong consistency and rate of convergence of the estimators are presented. Finally, their performances, for finite sample sizes, are illustrated by using simulated data.

Suggested Citation

  • Zouaoui Chikr-Elmezouar & Ibrahim M. Almanjahie & Ali Laksaci & Mustapha Rachdi, 2019. "FDA: strong consistency of the NN local linear estimation of the functional conditional density and mode," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(1), pages 175-195, January.
    • Handle: RePEc:taf:gnstxx:v:31:y:2019:i:1:p:175-195
    DOI: 10.1080/10485252.2018.1538450
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    Cited by:

    1. Ibrahim M. Almanjahie & Zouaoui Chikr Elmezouar & Ali Laksaci & Mustapha Rachdi, 2021. "Smooth k NN Local Linear Estimation of the Conditional Distribution Function," Mathematics, MDPI, vol. 9(10), pages 1-14, May.
    2. Ibrahim M. Almanjahie & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Estimating the Conditional Density in Scalar-On-Function Regression Structure: k -N-N Local Linear Approach," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    3. 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.
    4. Mustapha Rachdi & Ali Laksaci & Zoulikha Kaid & Abbassia Benchiha & Fahimah A. Al‐Awadhi, 2021. "k‐Nearest neighbors local linear regression for functional and missing data at random," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 42-65, February.

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