Renewable estimation in linear expectile regression models with streaming data sets

TL;DR

This paper introduces a novel online renewable expectile regression method for streaming data that efficiently detects heteroscedasticity and inhomogeneous effects, offering superior computational performance and statistical accuracy.

Contribution

The paper proposes a new expectile-based online renewable regression approach that reduces storage needs and improves computational efficiency while maintaining statistical properties.

Findings

Method achieves comparable accuracy to oracle estimators.

Significantly reduces computational time and storage requirements.

Performs well in numerical experiments and real-data applications.

Abstract

Streaming data often exhibit heterogeneity due to heteroscedastic variances or inhomogeneous covariate effects. Online renewable quantile and expectile regression methods provide valuable tools for detecting such heteroscedasticity by combining current data with summary statistics from historical data. However, quantile regression can be computationally demanding because of the non-smooth check function. To address this, we propose a novel online renewable method based on expectile regression, which efficiently updates estimates using both current observations and historical summaries, thereby reducing storage requirements. By exploiting the smoothness of the expectile loss function, our approach achieves superior computational efficiency compared with existing online renewable methods for streaming data with heteroscedastic variances or inhomogeneous covariate effects. We establish the consistency and asymptotic normality of the proposed estimator under mild regularity conditions, demonstrating that it achieves the same statistical efficiency as oracle estimators based on full individual-level data. Numerical experiments and real-data applications demonstrate that our method performs comparably to the oracle estimator while maintaining high computational efficiency and minimal storage costs.