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Two-stage regression spline modeling based on local polynomial kernel regression

Author

Listed:
  • Hamid Mraoui

    (Mohammed First University)

  • Ahmed El-Alaoui

    (Moulay Ismail University of Meknès)

  • Souad Bechrouri

    (Mohammed First University)

  • Nezha Mohaoui

    (Moulay Ismail University of Meknès)

  • Abdelilah Monir

    (Moulay Ismail University of Meknès)

Abstract

This paper introduces a new nonparametric estimator of the regression based on local quasi-interpolation spline method. This model combines a B-spline basis with a simple local polynomial regression, via blossoming approach, to produce a reduced rank spline like smoother. Different coefficients functionals are allowed to have different smoothing parameters (bandwidths) if the function has different smoothness. In addition, the number and location of the knots of this estimator are not fixed. In practice, we may employ a modest number of basis functions and then determine the smoothing parameter as the minimizer of the criterion. In simulations, the approach achieves very competitive performance with P-spline and smoothing spline methods. Simulated data and a real data example are used to illustrate the effectiveness of the method proposed in this paper.

Suggested Citation

  • Hamid Mraoui & Ahmed El-Alaoui & Souad Bechrouri & Nezha Mohaoui & Abdelilah Monir, 2025. "Two-stage regression spline modeling based on local polynomial kernel regression," Computational Statistics, Springer, vol. 40(1), pages 383-403, January.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01498-x
    DOI: 10.1007/s00180-024-01498-x
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, June.
    2. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    3. Lu, Zhan-Qian, 1996. "Multivariate Locally Weighted Polynomial Fitting and Partial Derivative Estimation," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 187-205, November.
    4. Andrews, Donald W. K., 1991. "Asymptotic optimality of generalized CL, cross-validation, and generalized cross-validation in regression with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 359-377, February.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, June.
    6. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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