Robust Composite Quantile Regression with Large‐scale Streaming Data Sets

Abstract Composite quantile regression (CQR) has advantages in robustness and high estimation efficiency. In modern statistical learning, we often encounter streaming data sets with unbounded cumulative data sizes. However, limited computer memory and non‐smoothness of CQR objective function pose challenges to methods and algorithms. An interesting issue is how to implement CQR in the streaming data setting. To address this issue, this article first constructs a smooth CQR, and then an online renewable CQR procedure is proposed. In theory, the oracle property of the proposed renewable estimator is established, which gives theoretical guarantees. Numerical experiments also confirm the proposed methods.