Theoretical Study of Fourier Series Estimator in Semiparametric Regression for Longitudinal Data Based on Weighted Least Square Optimization

Abstract

Semiparametric regression approach is a combination of two components, namely the parametric regression component and the nonparametric regression component. The data used in this study is longitudinal data. Longitudinal data is data obtained from repeated observations of each subject at different time intervals. This data correlates to the same subject and is independent between different subjects. In this study the parametric component is assumed to be linear and the nonparametric component is approximated by the Fourier Series function. In this study, we determine the estimator for semiparametric regression parameters longitudinal data using Weighted Least Square (WLS). In the semiparametric regression based on Fourier series estimator for longitudinal data, the optimal oscillation parameter k will be selected. To get the estimation of model parameters, the WLS optimization is performed and GCV method is used to determine the optimal k. After obtaining the optimal oscillation parameters from the minimum GCV, the oscillation parameters are used again in the Fourier series semiparametric regression modeling. The criteria for goodness of the model use and the value of MSE. The best model is a model that has a high value and a small MSE value.