Robust empirical likelihood inference for partially linear varying coefficient models with longitudinal data

Abstract

This paper presents a robust empirical likelihood procedure based on the exponential squared loss (ESL) function and leverage-based weights for the partially linear varying coefficient model with longitudinal data. The proposed method simultaneously solves the problems of correlation structure of longitudinal data and the existence of outliers, and achieves robustness and efficiency by introducing an appropriate data-driven tuning parameter. More importantly, profit from the QR decomposition technique, our method allows the parametric and nonparametric parts of the models to be estimated separately, which can avoid the mutual influence between them and make the implementation easier. Under some mild conditions, the large sample theoretical properties of the robust empirical likelihood approach are established. Simulation studies and a real data analysis are also carried out to assess and illustrate the finite sample performance.