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

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

Applied Mathematics and Computation, 2023, vol. 436, issue C

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.

Keywords: Variable-knot spline regression; Tensor product B-splines; Greville abscissae; Control polygon; Generalized non-linear models (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005677

DOI: 10.1016/j.amc.2022.127493

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