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

Hamid Mraoui (), Ahmed El-Alaoui (), Souad Bechrouri (), Nezha Mohaoui () and Abdelilah Monir ()
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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

Computational Statistics, 2025, vol. 40, issue 1, No 16, 383-403

Abstract: 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.

Keywords: Local polynomial regression; Bandwidth; B-spline; Blossoming; Quasi-interpolation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01498-x

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