Estimation of noisy cubic spline using a natural basis

Azzouz Dermoune, Cristian Preda

Abstract


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.

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