| Issue |
ESAIM: COCV
Volume 9, February 2003
|
|
|---|---|---|
| Page(s) | 553 - 562 | |
| DOI | https://doi.org/10.1051/cocv:2003026 | |
| Published online | 15 September 2003 | |
Statistical Estimates for Generalized Splines
1
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; magnus@ece.gatech.edu.
2
Department of Mathematics and Statistics,
Texas Tech University, Lubbock, TX 79409, USA; martin@math.ttu.edu.
Received:
29
March
2001
Revised:
27
November
2002
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.
Mathematics Subject Classification: 93-xx
Key words: Optimal control / smoothing splines / linear systems / interpolation.
© EDP Sciences, SMAI, 2003
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