Knot-Placement to Avoid over Fitting in B-Spline Scedastic Smoothing

Abstract

This article deals with knot-placement in B-spline scedastic smoothing. We commonly fit B-spline using knots between which each interval is the same width. The number of knots is selected by applying an information criterion with an optimization algorithm. In order to avoid over fitting with this method, we consider other arrangements based on the number of sample points in each interval. We choose knots such that each interval contains about the same number of samples. These knot placement schemes are compared through the Monte Carlo simulation.

Keywords:

• Equidistant arrangement
• Equipotent arrangement
• Information criterion
• Nonparametric regression
• Optimization algorithm
• Smoothing parameter

Acknowledgments

The authors wish to thank Dr. John Cologne, Radiation Effects Research Foundation, Professor Yasunori Fujikoshi, Hiroshima University, for their helpful comments, and also the referee for their useful comments. This work partially completed while Dr. Yanagihara was a graduate student of Hiroshima University.