Sequential adaptive nonparametric regression via h-splines

Abstract

The hybrid spline method (H‐spline) introduced by Dias (1994) is a hybrid method of curve estimation which combines ideas of regression spline and smoothing spline methods. In the context of nonparametric regression and by using basis functions (B‐splines), this method is much faster than smoothing spline methods (e.g. (Wahba, 1990)). The H‐spline algorithm is designed to compute a solution of the penalized least square problem, where the smoothing parameter is updated jointly with the number of basis functions in a performance‐oriented iteration. The algorithm increases the number of basis functions by one until the partial affinity between two consecutive estimates satisfies a constant determined empirically

Keywords:

• penalized least squares
• B‐splines
• smoothing splines
• Hellinger distance
• generalized cross validation
• hybrid splines