Composite quantile regression for correlated data

This study investigates composite quantile regression estimation for longitudinal data on the basis of quadratic inference functions. By incorporating the correlation within subjects, the proposed CQRQIF estimator has the advantages of both robustness and high estimation efficiency for a variety of error distributions. The theoretical properties of the resulting estimators are established. Given that the objective function is non-smooth and non-convex, an estimation procedure based on induced smoothing is developed. It is proved that the smoothed estimator is asymptotically equivalent to the original estimator. The weighted composite quantile regression estimation is also proposed to improve the estimation efficiency further in some situations. Extensive simulations are conducted to compare different estimators, and a real data analysis is used to illustrate their performances.