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

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