Communication‐efficient low‐dimensional parameter estimation and inference for high‐dimensional Lp$$ {L}^p $$‐quantile regression
针对分布式高维数据，提出两种通信高效的Lp分位数回归估计方法，用于估计低维参数，并通过模拟和犯罪数据分析验证其有效性。
Abstract The ‐quantile regression generalizes both quantile regression and expectile regression, and has become popular for its robustness and effectiveness especially when . In this paper, we consider the data that are inherently distributed and propose two distributed ‐quantile regression estimators for a preconceived low‐dimensional parameter in the presence of high‐dimensional extraneous covariates. To handle the impact of high‐dimensional nuisance parameters, we first investigate regularized projection score for estimating low‐dimensional parameter of main interest in ‐quantile regression. To deal with the distributed data, we further propose two communication‐efficient surrogate projection score estimators and establish their theoretical properties. The finite‐sample performance of the proposed estimators is studied through simulations and an application to Communities and Crime data set is also presented.