Online updating Huber robust regression for big data streams

Big data streams have garnered significant attention in multiple industries. However, the immense volume and the presence of outliers in high-velocity streaming data pose great challenges to its analysis. To address these concerns, this paper introduces a novel Online Updating Huber Robust Regression algorithm. By efficiently capturing the salient features of new data subsets, a computationally efficient online updating estimator is proposed without the need for storing historical data. Furthermore, by incorporating Huber regression into its framework, the estimator exhibits robustness to heavy-tailed, heterogeneous as well as outlier-contaminated data. Theoretically, the proposed online updating estimator is asymptotically equivalent to an Oracle estimator derived from the entire dataset. Extensive numerical simulations and a real-world data analysis have been conducted to demonstrate the effectiveness and practicality of the proposed method.