Data smoothing by splines with free knots
- 27 Downloads
A smoother based on an adaptive cubic model [1, 2] and splines with free knots is proposed. The model uses three reference data points and two parameters of control for estimation of a near optimal position of knots at the axis x in autotracking mode. The data points are prethinned and corrected by local linear fitting. The coefficient table is obtained by standard spline procedure. The efficiency and the stability of the smoother w.r.t. random errors are shown on real noisy data.
PACS numbers02.30.-f 02.60.-x 02.60.Gf
Unable to display preview. Download preview PDF.
- 1.N. D. Dikoussar, “Local Cubic Approximation and Smoothing of Curves in Adaptation Mode,” JINR Commun. P10-99-168 (Dubna, 1999); N. D. Dikoussar, “A Local Cubic Smoothing in an Adaptation Mode,” JINR Preprint E10-2001-48 (Dubna, 2001).Google Scholar
- 4.J. Friedman, A Variable Span Smoother, SLAC PUB-3477 (Stanford, 1984).Google Scholar
- 5.B. W. Silverman, “A Fast and Efficient Cross-Validation Method for Smoothing Parameter Choice in Spline Regression,” J. Amer. Statist. Assn. 19 (1984).Google Scholar
- 6.N. D. Dikoussar, “Discrete Projective Transformations on the Coordinate Plane,” Mathem. Model. 1(3), 50–64 (1991).Google Scholar
- 9.Cs. Török and N. D. Dikoussar, “MS.NET Components for Piecewise-Cubic Approximation,” JINR Commun. P10-2004-202 (Dubna, 2004).Google Scholar
- 10.M. Révayová and Cs. Török, “Piecewise Approximation and Neural Networks,” Kibernetika 43(4), (2007).Google Scholar
- 11.The European Phys. J. C. Review of Particle Physics (Springer, 2000), p. 235.Google Scholar