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Statistical Estimates for Generalized Splines

Published online by Cambridge University Press:  15 September 2003

Magnus Egerstedt  and
Clyde Martin
Magnus Egerstedt
Affiliation:
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; magnus@ece.gatech.edu.
Clyde Martin
Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA; martin@math.ttu.edu.
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Abstract

In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.

Keywords

Optimal controlsmoothing splineslinear systemsinterpolation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 553 - 562
Copyright
© EDP Sciences, SMAI, 2003

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References

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