Semiparametric regression based on three forms of trigonometric function in fourier series estimator

The semiparametric regression is one of the three forms of regression analysis which is made up of parametric and nonparametric. While the parametric is based on linear estimator, this nonparametric component is an innovation. This research proposes all the possible trigonometric basis usually used in Fourier series as nonparametric component estimator, its advantage, which includes its ability to overcome data with oscillation patterns. This study discusses nonparametric regression based on complete and sine Fourier series. Both estimators are developed using the cosine Fourier series concept. The outputs are two estimators which are used for parametric and nonparametric components with the corresponding form in semiparametric regression. In addition, all of these can be applied in real problems, and the best estimator is determined based on the smallest GCV and MSE for an oscillation parameter which gives the highest coefficient of determination for the selected one.