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Functional data analysis: estimation of the relative error in functional regression under random left-truncation model

Author

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  • Belkais Altendji
  • Jacques Demongeot
  • Ali Laksaci
  • Mustapha Rachdi

Abstract

In this paper, we investigate the relationship between a functional random covariable and a scalar response which is subject to left-truncation by another random variable. Precisely, we use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional truncated data. Under some standard assumptions in functional data analysis, we establish the almost sure consistency, with rates, of the constructed estimator as well as its asymptotic normality. Then, a simulation study, on finite-sized samples, was carried out in order to show the efficiency of our estimation procedure and to highlight its superiority over the classical kernel estimation, for different levels of simulated truncated data.

Suggested Citation

  • Belkais Altendji & Jacques Demongeot & Ali Laksaci & Mustapha Rachdi, 2018. "Functional data analysis: estimation of the relative error in functional regression under random left-truncation model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 472-490, April.
    • Handle: RePEc:taf:gnstxx:v:30:y:2018:i:2:p:472-490
    DOI: 10.1080/10485252.2018.1438609
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    Cited by:

    1. Feriel Bouhadjera & Mohamed Lemdani & Elias Ould Saïd, 2023. "Strong uniform consistency of the local linear relative error regression estimator under left truncation," Statistical Papers, Springer, vol. 64(2), pages 421-447, April.
    2. Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.
    3. 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.
    4. Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.

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