  In this paper, we focus on distributed estimation and support recovery for
high-dimensional linear quantile regression. Quantile regression is a popular
alternative tool to the least squares regression for robustness against
outliers and data heterogeneity. However, the non-smoothness of the check loss
function poses big challenges to both computation and theory in the distributed
setting. To tackle these problems, we transform the original quantile
regression into the least-squares optimization. By applying a double-smoothing
approach, we extend a previous Newton-type distributed approach without the
restrictive independent assumption between the error term and covariates. An
efficient algorithm is developed, which enjoys high computation and
communication efficiency. Theoretically, the proposed distributed estimator
achieves a near-oracle convergence rate and high support recovery accuracy
after a constant number of iterations. Extensive experiments on synthetic
examples and a real data application further demonstrate the effectiveness of
the proposed method.
