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An estimating parameter of nonparametric regression model based on smoothing techniques

This paper studies the estimating parameter of a nonparametric regression model that consists of the function of independent variables and observation of dependent variables. The smoothing spline, penalized spline, and B-spline methods in a class of smoothing techniques are considered for estimating the unknown parameter on nonparametric regression model. These methods use a smoothing parameter to control the smoothing performance on data set by using a cross-validation method. We also compare these methods by fitting a nonparametric regression model on simulation data and real data. The nonlinear model is a simulation data which is generated in two different models in terms of mathematical function based on statistical distribution. According to the results, the smoothing spline, the penalized spline, and the B-spline methods have a good performance to fit nonlinear data by considering the hypothesis testing of biased estimator. However the penalized spline method shows the minimum mean square errors on two models. As real data, we use the data from a light detection and ranging (LIDAR) experiment that contained the range distance travelled before the light as an independent variable and the logarithm of the ratio of received light from two laser sources as a dependent variable. From the mean square errors of fitting data, the penalized spline again shows the minimum values.