An application of various nonparametric techniques by nonparametric regression splines

Abstract

In this paper we made a comparison study between regression spline, penalized spline, and their Bayesian versions: adaptive Bayesian regression spline and Bayesian penalized spline with a different number of observations. For this purpose we made a simulation study with four different functions with six positions. For regression and penalized splines the important problems are the knot selection and selection of smoothing parameter. For both techniques we used equidistant knot selection as a basis method in regression techniques. The purpose of using different number of sampled observations is to analyze the behavior of utilized techniques. All results are compared with each other by mean value of the MSE (mean squared error). The penalized spline showed one of the best results between spline techniques and their Bayesian versions.