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Cross-Validated Functional Generalized Partially Linear Single-Functional Index Model

Author

Listed:
  • Mustapha Rachdi

    (Laboratory AGEIS, Grenoble Alps University, UFR SHS, BP. 47, Cedex 09, 38040 Grenoble, France
    These authors contributed equally to this work.)

  • Mohamed Alahiane

    (Complex Systems Modeling Laboratory, National School of Applied Sciences, Cadi Ayyad University, Av. Abdelkrim Khattabi, BP. 575, Marrakesh 40000, Morocco
    These authors contributed equally to this work.)

  • Idir Ouassou

    (Complex Systems Modeling Laboratory, National School of Applied Sciences, Cadi Ayyad University, Av. Abdelkrim Khattabi, BP. 575, Marrakesh 40000, Morocco
    These authors contributed equally to this work.)

  • Abdelaziz Alahiane

    (SmartICT Lab, ENSAO, Mohamed Premier University, Oujda 60000, Morocco
    These authors contributed equally to this work.)

  • Lahoucine Hobbad

    (Complex Systems Modeling Laboratory, National School of Applied Sciences, Cadi Ayyad University, Av. Abdelkrim Khattabi, BP. 575, Marrakesh 40000, Morocco
    These authors contributed equally to this work.)

Abstract

In this paper, we have introduced a functional approach for approximating nonparametric functions and coefficients in the presence of multivariate and functional predictors. By utilizing the Fisher scoring algorithm and the cross-validation technique, we derived the necessary components that allow us to explain scalar responses, including the functional index, the nonlinear regression operator, the single-index component, and the systematic component. This approach effectively addresses the curse of dimensionality and can be applied to the analysis of multivariate and functional random variables in a separable Hilbert space. We employed an iterative Fisher scoring procedure with normalized B-splines to estimate the parameters, and both the theoretical and practical evaluations demonstrated its favorable performance. The results indicate that the nonparametric functions, the coefficients, and the regression operators can be estimated accurately, and our method exhibits strong predictive capabilities when applied to real or simulated data.

Suggested Citation

  • Mustapha Rachdi & Mohamed Alahiane & Idir Ouassou & Abdelaziz Alahiane & Lahoucine Hobbad, 2024. "Cross-Validated Functional Generalized Partially Linear Single-Functional Index Model," Mathematics, MDPI, vol. 12(17), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2649-:d:1464349
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    References listed on IDEAS

    as
    1. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    2. Chin-Shang Li & Minggen Lu, 2018. "A lack-of-fit test for generalized linear models via single-index techniques," Computational Statistics, Springer, vol. 33(2), pages 731-756, June.
    3. Ping Yu & Jiang Du & Zhongzhan Zhang, 2020. "Single-index partially functional linear regression model," Statistical Papers, Springer, vol. 61(3), pages 1107-1123, June.
    4. Ali Laksaci & Zoulikha Kaid & Mohamed Alahiane & Idir Ouassou & Mustapha Rachdi, 2023. "Non parametric estimations of the conditional density and mode when the regressor and the response are curves," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(13), pages 4659-4674, July.
    5. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
    6. Peng Lai & Ye Tian & Heng Lian, 2014. "Estimation and variable selection for generalised partially linear single-index models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 171-185, March.
    7. Ruiyuan Cao & Jiang Du & Jianjun Zhou & Tianfa Xie, 2020. "FPCA-based estimation for generalized functional partially linear models," Statistical Papers, Springer, vol. 61(6), pages 2715-2735, December.
    8. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    9. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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