Sequential adaptive nonparametric regression via H-splines

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.