Efficient Inference about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

This article considers the estimation for the partially linear varying coefficient model with random effect. This article proposes to use the estimators for the variance component and profile weighted semi-parametric least squares (WSLSE) techniques to estimate the parametric component efficiently and to establish its efficiency and asymptotic properties. The proposed estimator is proved to be more efficient than that naive estimation with working independence error structure. Some Monte Carlo simulations are conducted to examine the finite sample performance. Moreover, from the empirical study, the newly proposed procedure performs well in moderate-sized samples.