Three form fourier series estimator semiparametric regression for longitudinal data

Abstract

Analysis of regressionis one technique that is often used in statistical analysis. There are three regression analysis approaches, such as parametric regression, nonparametric regression and semiparametric regression. Semiparametric regression consists of parametric components and nonparametric components. Parametric component that used such as linear estimator and nonparametric component by using a Fourier series estimator. Semiparametric regression approach that use Fourier series, have an advantages which is can resolve oscillation data pattern. This study compares the three Fourier series estimators such as sine, cosine, and combination between cosine and sine or complete estimator for longitudinal data. Longitudinal data can explain more complete information than cross section data or time series data. The purpose of this study is to introduce another Fourier series for the application of electricity consumption in Madura island. The results of this study indicated the optimal model in predicting electricity consumption in Madura island. The best estimator is the Fourier series estimator with the smallest Generalized Cross Validation (GCV) and Mean Square Error (MSE), and the biggest determination coefficient values by considering the parsimony of the model.