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On the equivalence of two stochastic approaches to spline smoothing

Published online by Cambridge University Press:  14 July 2016

Craig F. Ansley  and
Robert Kohn
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Abstract

Wahba (1978) and Weinert et al. (1980), using different models, show that an optimal smoothing spline can be thought of as the conditional expectation of a stochastic process observed with noise. This observation leads to efficient computational algorithms. By going back to the Hilbert space formulation of the spline minimization problem, we provide a framework for linking the two different stochastic models. The last part of the paper reviews some new efficient algorithms for spline smoothing.

Keywords

SIGNAL EXTRACTIONDIFFUSE PRIORSTOCHASTIC DIFFERENTIAL EQUATIONNON-LINEAR REGRESSIONKALMAN FILTER
Type
Part 7—Algorithms and Computations
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 391 - 405
Copyright
Copyright © 1986 Applied Probability Trust 

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