Copula based composite quantile regression for longitudinal data and variable selection

Abstract

Composite quantile regression (CQR) is a good alternative of the mean regression, becauseof its robustness and efficiency. As is well known, longitudinal data is characterized by within-subject correlation, and if the correlation can be correctly incorporated in the estimation procedure, the efficiency will be improved. Hence, how to specify the correlation structure in CQR with longitudinal data is an interesting issue. We propose a new approach that uses copula to account for intra-subject dependence, and by using the copula based covariance matrix, efficient and unbiased CQR estimating equations are constructed. As a specific application, a smooth-threshold CQR estimation equation is proposed for variable selection. Our proposed new methods are flexible, and can provide efficient estimation. The properties of the proposed methods are established theoretically, and assessed numerically through simulation studies and real data analysis.