Nonparametric regression curve estimation using mixed spline truncated and kernel estimator for longitudinal data

Abstract

Nonparametric regression is a regression model approach that can be used if the pattern of the relationship between response and predictor variable is unknown. One of the most widely used nonparametric regression models is spline truncated, which has very good ability in handling data whose behavior changes at sub-specified intervals. While the kernel estimator is used to model data that does not have a specific pattern. Nonparametric regression models used by researchers have tended to assume that the pattern of the relationship between each predictor and response variable has the same pattern so that only one form of estimator is used, but in some applications the pattern of relationship between each predictor and response variable can be different from one another. In this condition are advised to use a mixed estimator for nonparametric regression curve estimation. However, the existing mixed estimator is only limited to cross section data. Theoretically mixed spline truncated and kernel estimators can be generalized to longitudinal data, which is repeated observation data in an experimental unit. The purpose of this study is to obtain nonparametric regression curve estimation using mixed spline truncated and kernel estimator for longitudinal data, it is done by completing the Weighted Least Square (WLS) optimization. The selection of the best model based on optimal knots and bandwidth for mixed spline truncated and kernel estimators was obtained using minimum Generalized Cross Validation (GCV) values.