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Geometrically designed variable knot splines in generalized (non-)linear models

Author

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  • Dimitrova, Dimitrina S.
  • Kaishev, Vladimir K.
  • Lattuada, Andrea
  • Verrall, Richard J.

Abstract

In this paper we extend the GeDS methodology, recently developed by Kaishev et al. [18] for the Normal univariate spline regression case, to the more general GNM/GLM context. Our approach is to view the (non-)linear predictor as a spline with free knots which are estimated, along with the regression coefficients and the degree of the spline, using a two stage algorithm. In stage A, a linear (degree one) free-knot spline is fitted to the data applying iteratively re-weighted least squares. In stage B, a Schoenberg variation diminishing spline approximation to the fit from stage A is constructed, thus simultaneously producing spline fits of second, third and higher degrees. We demonstrate, based on a thorough numerical investigation that the nice properties of the Normal GeDS methodology carry over to its GNM extension and GeDS favourably compares with other existing spline methods.

Suggested Citation

  • Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Lattuada, Andrea & Verrall, Richard J., 2023. "Geometrically designed variable knot splines in generalized (non-)linear models," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    • Handle: RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005677
    DOI: 10.1016/j.amc.2022.127493
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    References listed on IDEAS

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    1. Gu, Chong, 2014. "Smoothing Spline ANOVA Models: R Package gss," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i05).
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
    3. Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
    4. Kovács, Péter & Fekete, Andrea M., 2019. "Nonlinear least-squares spline fitting with variable knots," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 490-501.
    5. Yang, Lianqiang & Hong, Yongmiao, 2017. "Adaptive penalized splines for data smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 70-83.
    6. Shen X. & Ye J., 2002. "Adaptive Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 210-221, March.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
    8. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Penev, Spiridon I., 2008. "GeD spline estimation of multivariate Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3570-3582, March.
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