The Estimation of a Regression Curve by Using Mixed Truncated Spline and Fourier Series Models for Longitudinal Data

There has been increasing interest in mixed estimators in nonparametric regression, although so far these have only been used for cross-sectional data. This paper proposes a new method to estimate nonparametric regression curves for longitudinal data. It uses two estimators: a truncated spline and Fourier series. The estimation of the regression curve is completed by minimizing the penalized weighted least squares and weighted least squares. This article also includes the properties of the new mixed estimator, which is biased and linear in the observations. This study selects the model with the smallest generalized cross-validation value. The performance of the new method is demonstrated by a simulation study with different subjects and numbers of time points. We also apply the proposed approach to a dataset of stroke patients. This study proves that the mixed estimator provides better results than a single estimator.