Distributed Bootstrap Simultaneous Inference for High-Dimensional Quantile Regression

Abstract

Modern massive data with enormous sample size and tremendous dimensionality are usually impossible to process with a single machine. They are typically stored and processed in a distributed manner. In this paper, we propose a distributed bootstrap simultaneous inference for a high-dimensional quantile regression model using massive data. Meanwhile, a communication-efficient (CE) distributed learning algorithm is developed via the CE surrogate likelihood framework and ADMM procedure, which can handle the non-smoothness of the quantile regression loss and the Lasso penalty. We theoretically prove the convergence of the algorithm and establish a lower bound on the number of communication rounds ιmin that warrant statistical accuracy and efficiency. The distributed bootstrap validity and efficiency are corroborated by an extensive simulation study.

Keywords

• distributed statistical learning
• multiplier bootstrap
• quantile regression
• communication efficiency
• ADMM algorithm