Combined estimator fourier series and spline truncated in multivariable nonparametric regression

Multivariable additive nonparametric regression model is a nonparametric regression model that involves more than one predictor and has additively separable function on each predictor. There are many functions that can be used on nonparametric regression models, such as the kernel, splines, wavelets, local polynomial and fourier series. The purpose of this study is to obtain an estimator of multivariable additive nonparametric regression model. This research focuses on multivariable additive nonparametric regression model which is a combination between fourier series and spline truncated. The estimation method that be used to obtain the estimators is Penalized Least Square. This method requires the estimation of smoothing parameters in the optimization process to obtain the estimators of model. In this study, the derivation process for obtaining the estimator of multivariable additive nonparametric regression model has been successfully obtained, which consists of an estimator of fourier series and spline truncated. The results of this theoretical study shows that the Penalized Least Square method works simultaneously for obtaining the estimators of the smoothing parameter and nonparametric regression model parameters as a result of combining between fourier series and spline truncated which are additively separable.