Expectile Regression on Distributed Large-Scale Data

Large-scale data presents great challenges to data analysis due to the limited computer storage capacity and the heterogeneous data structure. In this article, we propose a distributed expectile regression model to resolve the challenges of large-scale data by designing a surrogate loss function and using the Iterative Local Alternating Direction Method of the Multipliers (IL-ADMM) algorithm, which is developed for the calculation of the proposed estimator. To obtain nice performance only after fewer rounds of communications, the proposed method only needs to solve an M-estimation problem on the master machine while the other working machines only to compute the gradients based on local data. Moreover, we show the consistency and the asymptotic normality of the proposed estimator, and illustrate the efficient proof by numerical simulations and positive analysis on the superconductor data.