City Research Online

Geometrically Designed Variable Knot Splines in Generalized (Non-)Linear Models

Dimitrova, D. S., Kaishev, V. K., Lattuada, L. & Verrall, R. J. (2017). Geometrically Designed Variable Knot Splines in Generalized (Non-)Linear Models.


In this paper we extend the GeDS methodology, recently developed by Kaishev et al. (2016) 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. The proposed GeDS GNM(GLM) methodology is extended to the multivariate case of more than one independent variable by utilizing tensor product splines and their related shape preserving variation diminishing property.

Publication Type: Article
Departments: Bayes Business School > Actuarial Science & Insurance
[thumbnail of Article_GeDS_GN(L)M.pdf]
Text - Draft Version
Download (1MB) | Preview
[thumbnail of Supplement.pdf]
Text - Supplemental Material
Download (1MB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login