A class of template splines

Abstract

A common frame of template splines that unifies the definitions of various spline families, such as smoothing, regression or penalized splines, is considered. The nonlinear nonparametric regression problem that defines the template splines can be reduced, for a large class of Hilbert spaces, to a parameterized regularized linear least squares problem, which leads to an important computational advantage. Particular applications of template splines include the commonly used types of splines, as well as other atypical formulations. In particular, this extension allows an easy incorporation of additional constraints, which is generally not possible in the context of classical spline families.