In this talk, we present a novel and communication-efficient approach for sparse and high-dimensional distributed data with the penalized expectile or quantile regression, which is realized by considering the proximal alternating direction method of multipliers (ADMM) algorithm on the master machine and the subgradient about local data on other worker machines. As for the communication efficiency, the proposed approach does not sacrifice any statistical accuracy and provably improves the estimation error obtained by centralized method, provided the penalty levels are chosen properly.