A Reproducing Kernel Perspective of Smoothing Spline Estimators

Bianconcini, Silvia (2008) A Reproducing Kernel Perspective of Smoothing Spline Estimators. Bologna, IT: Dipartimento di Scienze Statistiche "Paolo Fortunati", Alma Mater Studiorum Università di Bologna, p. 43. DOI 10.6092/unibo/amsacta/2430. In: Quaderni di Dipartimento. Serie Ricerche ISSN 1973-9346.
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Spline functions have a long history as smoothers of noisy time series data, and several equivalent kernel representations have been proposed in terms of the Green's function solving the related boundary value problem. In this study we make use of the reproducing kernel property of the Green's function to obtain an hierarchy of time-invariant spline kernels of different order. The reproducing kernels give a good representation of smoothing splines for medium and long length filters, with a better performance of the asymmetric weights in terms of signal passing, noise suppression and revisions. Empirical comparisons of time-invariant filters are made with the classical non linear ones. The former are shown to loose part of their optimal properties when we fixed the length of the filter according to the noise to signal ratio as done in nonparametric seasonal adjustment procedures.

Document type
Monograph (Working Paper)
Bianconcini, Silvia
equivalent kernels, nonparametric regression, Hilbert spaces, time series filtering, spectral properties Kernel equivalenti, regressione non parametrica, spazi di Hilbert, filtraggio di serie storiche, proprietà spettrali
Deposit date
12 Mar 2008
Last modified
16 May 2011 12:07

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