Robust and efficient estimating equations for longitudinal data partial linear models and its applications

Composite quantile regression (CQR) is a good alternative of the mean regression, because of its robustness and efficiency. In longitudinal data analysis, correlation structure plays an important role in improving efficiency. However, how to specify the correlation matrix in CQR with longitudinal data is challenging. We propose a new approach that uses copula to account for intra-subject dependence, and by using the copula based covariance matrix, robust and efficient CQR estimating equations are constructed for the partial linear models with longitudinal data. As a specific application, a copula based CQR empirical likelihood is proposed. Furthermore, it can also be used to develop a penalized empirical likelihood for variable selection. Our proposed new methods are flexible, and can provide robust and efficient estimation. The properties of the proposed methods are established theoretically, and assessed numerically through simulation studies.