We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on the nonparametric component and shrinkage penalty on the parametric components, which can achieve function smoothing and sparse estimation simultaneously. We e...

Smoothing with penalized splines calls for an automatic method to select the size of the penalty parameter λ . We propose a not well known smoothing parameter selection procedure: the L-curve method. AIC and (generalized) cross validation represent the most common choices in this kind of problems even if they indicate light smoothing when the data represent a smooth trend plus correlated noise....

This article proposes an automatic smoothing method for recovering discontinuous regression functions. The method models the target regression function with a series of disconnected cubic regression splines which partition the function’s domain. In this way discontinuity points can be incorporated in a fitted curve simply as the boundary points between adjacent splines. Three objective criteria...

A solution is presented to the problem of selecting sample points in an optimal fashion. These points are used for interpolation and smoothing procedures, and, in particular, we derive necessary optimality conditions for the sample points. An example is presented concerning generalized smoothing splines that illustrate the generality as well as the numerical feasibility of the proposed approach...