Mix local polynomial and spline truncated: the development of nonparametric regression model

Abstract

Regression analysis is a statistical method used to model response variables with predictor variables. The approach to regression analysis can be done by parametric, semiparametric and nonparametric. The nonparametric approach is more complex than parametric. Some nonparametric approaches include local and spline polynomial. Local polynomial is the development of the taylor series which has an arbited fixed point, while the splines are pieces of the spline function. In both spline and local polynomial modeling requires a smoothing parameterb determined by GCV (General Cross Validation) method. In this paper, we developed a method of combining local and spline polynomials. The parameter estimation uses the OLS (Ordinary Least Square) method, yielding an estimator (XTKhX)-1XTKhy, where X is a predictor variable with combination of polynomial and spline function, whereas Kh is a kernel function used for the combination of local polynomial and spline function.