Sparse and debiased lasso estimation and inference for high-dimensional composite quantile regression with distributed data

We consider the data are inherently distributed and focus on statistical learning in the presence of heavy-tailed and/or asymmetric errors. The composite quantile regression (CQR) estimator is a robust and efficient alternative to the ordinary least squares and single quantile regression estimators. Based on the aggregated and communication-efficient approaches, we propose two classes of sparse and debiased lasso CQR estimation and inference methods. Specifically, an aggregated L-1-penalized CQR esti-mator and a L-1-penalized communication-efficient CQR estimator are obtained firstly. To construct confidence intervals and make hypothesis testing, a unified debiasing framework based on smoothed decorrelated score equations is introduced to eliminate biases caused by lasso penalty. Finally, a hard-thresholding method is employed to ensure that the debiased lasso estimators are sparse. The convergence rates and asymp-totic properties of the proposed estimators are established and their performance is evaluated through simulations and a real-world dataset.

Automated summary

This paper investigates statistical learning in the presence of heavy-tailed and/or asymmetric errors by considering the inherent distribution of the data. The composite quantile regression (CQR) estimator is proposed as a robust and efficient alternative to the ordinary least squares and single quantile regression estimators. Two classes of sparse and debiased lasso CQR estimation and inference methods are proposed based on aggregated and communication-efficient approaches. The performance of the proposed estimators is evaluated through simulations and a real-world dataset.