Asymptotic normality for a local composite quantile regression estimator of regression function with truncated data

In this paper, we construct a local linear composite quantile regression (CQR) estimator of regression function for left-truncated data, which extends the CQR method to the left-truncated model. The asymptotic normality of the proposed estimator is also established. The estimator is much more efficient than the local linear regression estimator for commonly-used non-normal error distributions via simulations.