Optimal knot selection in spline regression using unbiased risk and generalized cross validation methods

Abstract

Spline regression is a nonparametric regression method that estimates data patterns that do not form certain patterns with the help of knots. The best model is obtained from the optimal knot. There are several methods that can be used to select optimal knots, including Generalized Cross-Validation (GCV) and Unbiassed Risk (UBR). The best model selection criteria used are based on the Mean Squared Error (MSE) and R-Square values. This study discusses the comparison of spline regression models using the UBR and GCV methods as a method for selecting optimal knots in data generation simulations. This research resulted in the best nonparametric spline regression model from the UBR method obtained by using three knots which produced an MSE value of 738.67 and R -Square of 85.65%. Whereas, the best nonparametric spline regression model of the GCV method was obtained using three knots which produced an MSE value of 121.43 and R-Square of 97.64%. It can be concluded that the more appropriate method used for the selection of optimal knot is the GCV method because it produces a smaller MSE value and a larger R-Square compared to the UBR method.