Gaussian copula based composite quantile regression in semivarying models with longitudinal data

This paper proposes a new efficient composite quantile regression (CQR) estimating function for the semivarying models with longitudinal data, which can incorporate the correlation structure between repeated measures via the Gaussian copula. Because the objective function is non-smooth and non-convex, the induced smoothing method is used to reduce computational burdens. It is proved that the smoothed estimator is asymptotically equivalent to the original estimator. Furthermore, a smooth-threshold efficient CQR estimating equation variable selection method is proposed. Because the new method can incorporate the correlation structure and inherit the good properties of CQR, it has the advantages of both robustness and high estimation efficiency. Simulation studies and real data analysis are also included to illustrate the finite sample performance of our methods.