Estimation of noisy cubic spline using a natural basis
  We define a new basis of cubic splines such that the coordinates of a natural cubic spline are sparse. We use it to analyse and to extend the classical Schoenberg and Reinsch result and to estimate a noisy cubic spline. We also discuss the choice of the smoothing parameter. All our results are illustrated graphically. 
Azzouz Dermoune and Cristian Preda
math.ST stat.TH