A Double Varying-coefficient Modeling Approach for Analyzing Longitudinal Observations

The identification of within-subject dependence is important for constructing efficient estimation in longitudinal data models. In this paper, we proposed a flexible way to study this dependence by using nonparametric regression models. Specifically, we considered the estimation of varying coefficient longitudinal data model with non-stationary varying coefficient autoregressive error process over observational time quantum. Based on spline approximation and local polynomial techniques, we proposed a two-stage nonparametric estimation for unknown functional coefficients and didn't not drop any observations in a hybrid least square loss framework. Moreover, we showed that the estimated coefficient functions are asymptotically normal and derived the asymptotic biases and variances accordingly. Monte Carlo studies and two real applications were conducted for illustrating the performance of our proposed methods.