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Explicit evaluation of the equivalent degrees of freedom of smoothing splines: A spectral factorization approach

Author(s):

G. De Nicolao, G. Ferrari-Trecate, G. Sparacino
Conference/Journal:

Mathematical Theory of Networks and Systems, Padova, Italy
Abstract:

Smoothing splines are commonly used to reconstruct an unknown continuous function given n discrete noisy sam­ ples. In the tuning of the regularization parameter, which controls the balance between smoothness and data­fit, the most computer­intensive part is the evaluation of the so­called ''equivalent degrees of freedom'' (EDOF) as a function of the regularization parameter. In the paper a closed­form expression of the asymptotic (as n goes to infinity) EDOF is obtained for the case of equally spaced data. The derivation is based on the reformulation of the spline smoothing problem as a Bayesian estimation prob­ lem. State­space methods, Kalman filtering, and spectral factorization techniques are used to show that the asymp­ totic EDOF can be obtained as the variance of a suitably defined stationary process. As a by­product of the main result, it is found that the asymptotic EDOF depend on the cube of the sampling interval.

Year:

1998
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@InProceedings { NicFer:1998:IFA_1758,
    author={G. De Nicolao and G. Ferrari-Trecate and G. Sparacino},
    title={{Explicit evaluation of the equivalent degrees of freedom of
	  smoothing splines: A spectral factorization approach}},
    booktitle={Mathematical Theory of Networks and Systems},
    pages={},
    year={1998},
    address={Padova, Italy},
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=1758}
}
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