A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data

It is well known that the composite quantile regression is a very useful tool for regression analysis. In longitudinal studies, it requires a correct specification of the covariance structure to obtain efficient estimation of the regression coefficients. However, it is a challenging task to specify the correlation matrix in composite quantile regression with longitudinal data. In this paper, we develop a new regression model to parameterize covariance structures by utilizing the modified Cholesky decomposition. Then, based on the estimated covariance matrix, efficient composite quantile estimating functions are constructed to produce more efficient estimates. Since the proposed estimating functions are discrete and non-convex, we apply the induced smoothing approach to achieve fast and accurate estimation of the regression coefficients. Furthermore, we derive the asymptotic distributions of the parameter estimations both in mean and covariance models. Finally, simulations and a real data analysis have demonstrated the robustness and efficiency of the proposed approach.