Renewable Online Expectile Regression for Heterogeneous Streaming Data with Abnormal Batches

2026-09-27

AI Summary

This study addresses the challenge of inter-batch heterogeneity in streaming data, often caused by anomalous batches or distribution shifts, which undermines existing methods reliant on batch homogeneity assumptions. To this end, this work proposes a renewable online expectile regression framework. It pioneers a dual strategy combining score test-based sequential monitoring and adaptive weighting, seamlessly integrated without requiring additional structural assumptions. Furthermore, Huber loss is incorporated to enhance robustness against heavy-tailed errors and outliers. Simulation studies and clinical data analyses demonstrate that the proposed method significantly improves estimation accuracy and model robustness under batch heterogeneity, enabling efficient real-time statistical inference.

Abstract

Streaming data, characterized by high volume, rapid arrival rates, and evolving distributions, have become increasingly prevalent in modern applications. Developing efficient and reliable estimation procedures is therefore essential for real-time statistical analysis. However, most existing online estimation methods rely on the assumption of batch homogeneity, which can be violated in practice due to abnormal batches, distributional shifts, or other forms of batch heterogeneity. To address this challenge, we develop renewable online expectile regression procedures for heterogeneous streaming data. Specifically, we propose two complementary strategies for handling abnormal batches: (1) a detection-based approach that employs a sequential monitoring mechanism based on score test statistics to identify and remove potentially abnormal batches; and (2) an adaptive-weighting approach that assigns data-driven weights to incoming batches, reducing the influence of abnormal or drifting batches while retaining information from reliable observations. Both strategies rely solely on score test statistics and can be seamlessly integrated into existing renewable estimation and inference frameworks without requiring additional structural assumptions. Furthermore, to enhance robustness against heavy-tailed errors and outliers, we replace the conventional l2 loss with the Huber loss and develop a robust extension of renew?able online expectile regression. Extensive simulation studies and analyses of clinical datasets demonstrate that the proposed methods achieve improved estimation accuracy and robustness in the presence of batch heterogeneity. Overall, the proposed framework provides a flexible and effective solution for renewable expectile regression in complex streaming data environments.

Problem

• streaming data
• expectile regression
• batch heterogeneity
• abnormal batches
• online estimation

Innovation

• Renewable online expectile regression
• Streaming data
• Abnormal batch detection
• Adaptive weighting
• Huber loss