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.

中文翻译：

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高维 Lp 分位数回归的通信高效低维参数估计和推理

这-分位数回归概括了分位数回归和期望回归，并因其鲁棒性和有效性而变得流行，特别是当。在本文中，我们考虑了本质上分布式的数据，并提出了两种分布式- 在存在高维无关协变量的情况下预先设想的低维参数的分位数回归估计器。为了处理高维干扰参数的影响，我们首先研究正则化投影分数，以估计主要感兴趣的低维参数-分位数回归。为了处理分布式数据，我们进一步提出了两种通信高效的替代投影分数估计器并建立了它们的理论特性。通过模拟研究了所提出的估计器的有限样本性能，并提出了在社区和犯罪数据集上的应用。