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Fast spline smoothing via spectral factorization concepts

Authors
  • Nicolao, Giuseppe De
  • Ferrari-Trecate, Giancarlo
  • Sparacino, Giovanni
Type
Published Article
Journal
Automatica
Publisher
Elsevier
Publication Date
Jan 01, 2000
Accepted Date
Apr 06, 2000
Volume
36
Issue
11
Pages
1733–1739
Identifiers
DOI: 10.1016/S0005-1098(00)00100-X
Source
Elsevier
Keywords
License
Unknown

Abstract

When tuning the smoothness parameter of nonparametric regression splines, the evaluation of the so-called degrees of freedom is one of the most computer-intensive tasks. In the paper, a closed-form expression of the degrees of freedom is obtained for the case of cubic splines and equally spaced data when the number of data tends to infinity. State-space methods, Kalman filtering and spectral factorization techniques are used to prove that the asymptotic degrees of freedom are equal to the variance of a suitably defined stationary process. The closed-form expression opens the way to fast spline smoothing algorithms whose computational complexity is about one-half of standard methods (or even one-fourth under further approximations).

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