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k‐Nearest neighbors local linear regression for functional and missing data at random

Author

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  • Mustapha Rachdi
  • Ali Laksaci
  • Zoulikha Kaid
  • Abbassia Benchiha
  • Fahimah A. Al‐Awadhi

Abstract

We combine the k‐Nearest Neighbors (kNN) method to the local linear estimation (LLE) approach to construct a new estimator (LLE‐kNN) of the regression operator when the regressor is of functional type and the response variable is a scalar but observed with some missing at random (MAR) observations. The resulting estimator inherits many of the advantages of both approaches (kNN and LLE methods). This is confirmed by the established asymptotic results, in terms of the pointwise and uniform almost complete consistencies, and the precise convergence rates. In addition, a numerical study (i) on simulated data, then (ii) on a real dataset concerning the sugar quality using fluorescence data, were conducted. This practical study clearly shows the feasibility and the superiority of the LLE‐kNN estimator compared to competitive estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:1:p:42-65
    DOI: 10.1111/stan.12224
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    References listed on IDEAS

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    1. Germán Aneiros & Ricardo Cao & Philippe Vieu, 2019. "Editorial on the special issue on Functional Data Analysis and Related Topics," Computational Statistics, Springer, vol. 34(2), pages 447-450, June.
    2. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    3. Firas Ibrahim & Ali Hajj Hassan & Jacques Demongeot & Mustapha Rachdi, 2020. "Regression model for surrogate data in high dimensional statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(13), pages 3206-3227, July.
    4. Baíllo, Amparo & Grané, Aurea, 2009. "Local linear regression for functional predictor and scalar response," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 102-111, January.
    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. 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.
    7. Mohammed Attouch & Ali Laksaci & Fatima Rafaa, 2019. "On the local linear estimate for functional regression: Uniform in bandwidth consistency," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 1836-1853, April.
    8. 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.
    9. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    10. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    11. 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.
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    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.

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