Semiparametric regression curve estimation for longitudinal data using mixed spline truncated and fourier series estimator

Abstract

Semiparametric regression is a regression approach that is used when the form of regression curve is assumed to be partly known and partly unknown. In the semiparametric regression model, the same type of estimation method is generally used for some or all of the predictor variables. There are many examples of data cases that have different patterns on each predictor variable, so if the data is forced to use only one form of estimator to estimate the regression curve, it will produce estimation that will not be appropriate to the data pattern. Therefore, a mixed estimator needs to be developed. However, mixed estimator in previous studies was only able to handle cross-sectional data. So this study uses longitudinal data that has advantages, one of which is estimation of each individual characteristic and time (period) characteristic are obtained separately in longitudinal data. Therefore, this study develops a mixed Spline Truncated and Fourier Series estimator in semiparametric regression for longitudinal data using the Weighted Least Square method. Estimation of the semiparametric regression model for longitudinal data using mixed estimator of Spline Truncated and Fourier Series is where D (K,m) = XA (K,m) + TB (K,m) + ZC (K,m). The selection of the best model is based on knot points and optimum oscillation parameters that should be selected optimally using minimum Generalized Cross Validation (GCV) value.