This paper concerns the distributed estimation and support recovery for the ultrahigh-dimensional linear regression model under potentially arbitrary noise distribution.The composite quantile regression is an efficient alternative to the least squares and provides robustness against heavy-tailed noises while maintaining reasonable efficiency under lighttailed ones. The highly non-smooth nature of the composite quantile regression loss poses new challenges to both the theoretical and computational development in the ultrahighdimensional distributed estimation setting. To this end, we cast the composite quantile regression into the least squares framework and propose a distributed algorithm based on an approximate Newton method. This algorithm is both computation-and communicationefficient and requires only gradient information to be communicated between the machines.We show the resultant distributed estimator attains a near-oracle rate after a constant number of communications, and provide theoretical guarantees for its estimation and support recovery accuracy. Extensive experiments are conducted to demonstrate the competitive empirical performance of our algorithm.

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