Communication-efficient sparse composite quantile regression for distributed data

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.

Automated summary

The composite quantile regression (CQR) estimator is a robust and efficient alternative in linear models, and can construct sparse CQR estimation. By proposing a penalized communication-efficient surrogate loss function, we only require the worker machines to compute the gradient and the central machine to solve a regular estimation problem to obtain the estimation. The performance of the proposed method is validated through simulation and application to real data set.