Equivalent reproducing kernels for smoothing spline predictors

We derive equivalent reproducing kernels of smoothing splines both in Sobolev and polynomial spaces. For the latter, we identify a density function or second order kernel, from which a hierarchy of higher order estimators is derived. These are shown to give excellent representations for the currently applied symmetric filters. The asymmetric weights are obtained by adapting the kernel functions to the length of the various filters, and a theoretical comparison is made with the classical estimators used in real time analysis. The former are shown to be superior in terms of signal passing, noise suppression and speed of convergence to the symmetric filter.