Online Updating Composite Quantile Regression for Streaming Data

ABSTRACT Data streams, characterized by high velocity and volume, pose significant challenges for real‐time data analysis. Online learning methods have become increasingly prominent for handling these challenges efficiently. In this paper, we consider an online renewable algorithm for composite quantile regression, which only needs to retain the key information in the historical data and update the summary statistics with the currently accessible data to obtain a renewable estimator. The proposed method is theoretically proven to be asymptotically equivalent to the oracle estimator derived from the entire dataset, offering advantages in computational and memory efficiency. Unlike previous approaches that impose constraints on batch numbers or data variance, our method is unconstrained by these factors. Meanwhile, numerical simulations and experiments on real data sets demonstrate that our estimator not only surpasses existing methods in handling both homogeneous and heterogeneous data but also performs better than traditional Quantile Regression in various scenarios. These findings highlight the suitability of our approach for real‐world streaming data applications.