A Unified Probabilistic View of Nonparametric Predictors via Reproducing Kernel Hilber Spaces

Bee Dagum, Estela ; Bianconcini, Silvia (2008) A Unified Probabilistic View of Nonparametric Predictors via Reproducing Kernel Hilber Spaces. Bologna, IT: Dipartimento di Scienze Statistiche "Paolo Fortunati", Alma Mater Studiorum Università di Bologna, p. 26. DOI 10.6092/unibo/amsacta/2519. In: Quaderni di Dipartimento. Serie Ricerche ISSN 1973-9346.
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We provide a common approach for studying several nonparametric estimators used for smoothing functional data. Linear filters based on different building assumptions are transformed into kernel functions via reproducing kernel Hilbert spaces. For each estimator, 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. In particular, we derive equivalent kernels of smoothing splines in Sobolev and polynomial spaces. The asymmetric weights are obtained by adapting the kernel functions to the length of the various filters, and a theoretical and empirical 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.

Document type
Monograph (Working Paper)
Bee Dagum, Estela
Bianconcini, Silvia
Polynomial kernel regression, smoothing splines, functional spaces, spectral properties, revisions Regressione kernel polinomiale, smoothing spline, spazi funzionali, revisioni
Deposit date
24 Sep 2008
Last modified
16 May 2011 12:09

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