Statistical Estimates for Generalized Splines
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; email@example.com.
2 Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA; firstname.lastname@example.org.
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