The performance of nonparametric regression for trend and seasonal pattern in longitudinal data

Recently, nonparametric regression does not only develop in cross section data but also in longitudinal data. Longitudinal data have repeated measurements in each subject. In the measurements for each subject sometimes there is a trend, seasonal, also combination between trend and seasonal data pattern. In this study, the performance of nonparametric regression estimators for longitudinal data related to model trend seasonal data pattern is compared by using Mean Square Error (MSE), Generalized Cross Validation (GCV) and determination coefficient value as goodness of indicator. The estimators that be used is truncated spline, Nadaraya Watson kernel, and Fourier series with include cosines and sines bases. This paper has contribution to introduce Fourier series, the new estimator for longitudinal data, as an alternative estimator for modeling trend and seasonal data. The result, the Fourier series estimator has the best performance indicators in modeling trend and seasonal data pattern for longitudinal data when compared with the estimator that be developed early in nonparametric regression for longitudinal data, such as spline and kernel. The result is important for data analysis in nonparametric regression for longitudinal data because there is data pattern with trend seasonal in many applications that need suitable estimator.