EXTENDING THE SMOOTHING SPLINE ESTIMATE

An extension of the one-parameter class of functionals considered in the Smoothing Spline Estimate framework is proposed to better deal with scaling problems or anisotropies of data to be approximated. In particular, a matrix, L, of regularizing parameters is introduced in place of the typical parameter lambda. By means of an appropriate coordinates transformation, the resulting variational problem can be rephrased in terms of the ''traditional'' Smoothing Spline Estimate method, and the Generalized Cross Validation technique can consequently be applied to find optimal values for L. Following this approach, numerical experiments have been performed on synthetic 2D data, and the results compared with those obtained with Smoothing Spline Estimate and Hyper Basis Function methods.