Multivariable Semiparametric Regression Model with Combined Estimator of Fourier Series and Kernel

Abstract

We purpose a combined estimator of Fourier series and Kernel on semiparametric regression. This method is used to resolve the problem of regression modeling, when the relationship between the response variable and the predictor variables most follow a certain pattern, partly have a repetitive pattern, and some others not follow a specific pattern. Moreover, this method depends on oscillation, smoothing parameter and bandwidth. The purpose of this research are to obtained the estimator of semiparametric regression model with combined estimator of Fourier series and Kernel using Penalized Least Square method (PLS). The result show that the PLS estimation produces the estimator of parametrik linier regression, the estimator of Fourier series, the estimator of Kernel, and also the combined estimator of Fourier series and Kernel in semiparametric regression model.