In this paper, we focus on distributed estimation and support recovery for
high-dimensional linear quantile regression. Quantile regression is a popular
alternative tool to the least squares regression for robustness against
outliers and data heterogeneity. However, the non-smoothness of the check loss
function poses big challenges to both computation and theory in the distributed
setting. To tackle these problems, we transform the original quantile
regression into the least-squares optimization. By applying a double-smoothing
approach, we extend a previous Newton-type distributed approach without the
restrictive independent assumption between the error term and covariates. An
efficient algorithm is developed, which enjoys high computation and
communication efficiency. Theoretically, the proposed distributed estimator
achieves a near-oracle convergence rate and high support recovery accuracy
after a constant number of iterations. Extensive experiments on synthetic
examples and a real data application further demonstrate the effectiveness of
the proposed method.

分布式估计和支持恢复在高维线性分位数回归中具有重要意义，本文通过将原始分位数回归转化为最小二乘优化问题，并应用双平滑方法，提出了一种新的分布式方法来解决此类问题，在保证计算和通信效率的同时能够实现接近 Oracle 收敛速度和高支持恢复精度的估计结果。通过对合成实例和真实数据应用的大量实验，验证了该方法的有效性。

分布式高维分位数回归：估计效率与支持恢复

Distributed High-Dimensional Quantile Regression: Estimation Efficiency  and Support Recovery

In this paper, we consider estimation of the conditional mode of an outcome
variable given regressors. To this end, we propose and analyze a
computationally scalable estimator derived from a linear quantile regression
model and develop asymptotic distributional theory for the estimator.
Specifically, we find that the pointwise limiting distribution is a scale
transformation of Chernoff's distribution despite the presence of regressors.
In addition, we consider analytical and subsampling-based confidence intervals
for the proposed estimator. We also conduct Monte Carlo simulations to assess
the finite sample performance of the proposed estimator together with the
analytical and subsampling confidence intervals. Finally, we apply the proposed
estimator to predicting the net hourly electrical energy output using Combined
Cycle Power Plant Data.

本文提出和分析了一种基于线性分位数回归模型的条件模估计量，并开发了其渐近分布理论。同时构建了分析和子采样法置信区间，并通过蒙特卡洛模拟评估了估计量和置信区间的有限样本性能。最后，将该估计量运用于预测联合循环发电厂数据的净小时电能输出。