An estimated general cross validation function for periodic control theoretic smoothing splines

Abstract

In this paper, a method is developed for estimating the optimal smoothing parameter ε for periodic control theoretic smoothing splines. The procedure is based on general cross validation (GCV) and requires no a priori information about the underlying curve or level of noise in the measurements. The optimal ε is the minimizer of an estimated GCV cost function, which is derived based on a discretization of the L 2 smoothing problem for periodic control theoretic smoothing splines. © 2010 Springer-Verlag Berlin Heidelberg.