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

Optimal subsampling algorithm for composite quantile regression with distributed data