Optimal subsampling algorithm for composite quantile regression with distributed data

For massive data stored on multiple machines, we propose a distributed subsampling procedure for the composite quantile regression. By establishing the consistency and asymptotic normality of the composite quantile regression estimator from a general subsampling algorithm, we derive the optimal subsampling probabilities and the optimal allocation sizes under the L-optimality criteria. A two-step algorithm is developed to approximate the optimal subsampling procedure. The proposed methods are illustrated through numerical experiments on simulated and real datasets.