Composite quantile regression (CQR) estimator is a robust and efficient alternative to the M-estimator and ordinary quantile regression estimator in linear models. In order to construct sparse CQR estimation in the presence of distributed data, we propose a penalized communication-efficient surrogate loss function that is computationally superior to the original global loss function. The proposed method only needs the worker machines to compute the gradient based on local data without a penalty and the central machine to solve a regular estimation problem. We prove that the estimation errors based on the proposed method match the estimation error bound of the centralized method by analyzing the entire data set simultaneously. A modified alternating direction method of multipliers algorithm is developed to efficiently obtain the sparse CQR estimator. The performance of the proposed estimator is studied through simulation, and an application to a real data set is also presented.

复合分位数回归 (CQR) 估计器是M-估计器和线性模型中的普通分位数回归估计器。为了在存在分布式数据的情况下构建稀疏 CQR 估计，我们提出了一种惩罚通信高效的代理损失函数，该函数在计算上优于原始全局损失函数。所提出的方法只需要工作机器基于本地数据计算梯度而没有惩罚，并且中心机器解决常规估计问题。我们通过同时分析整个数据集证明了基于所提出方法的估计误差与集中方法的估计误差界限相匹配。为了有效地获得稀疏CQR估计量，开发了一种改进的乘法交替方向方法。通过仿真研究了所提出的估计器的性能，