Comparison of Estimating Parameter in Parametric Regression, Nonparametric Regression, and Semiparametric Regression models in Case of Two Explanatory Variables

Abstract

In this paper, we compare the estimating parameter in the parametric regression model, nonparametric regression model, and semiparametric regression model between response variable and two explanatory varaibles. The parametric regression model uses the least square method for estimating parameter. The penalized spline method based on nonparametric regression method is proposed for estimating function of nonparametric regression model, and semiparametric regression model. The minimum of Mean Square Error (MSE) is a criterion for choosing the optimal model. Here, we simulate the response variable and two explanatory variables that correlated a nonlinear data based on uniform distribution. ??The real data can be applied of these models to illustrate the methodology.?? The estimated values of nonparametric regression model is a good performance in both of simulated data and real data.

Keywords: nonparametric regression model, parametric regression model, penalized spline

method, semiparametric regression model