Renewable estimation in expectile regression model with streaming data sets

Abstract

Streaming data continually expands over time, making it challenging to apply traditional expectile regression methods due to memory limitations. Expectile regression is advantageous for studying the entire conditional distribution of the response to a predictor, but handling streaming data requires innovative approaches. This paper proposes an online renewable expectile regression strategy, which updates the estimator using both the current data and summary statistics from historical data. An ADMM algorithm is employed to efficiently compute the proposed estimator. We establish the consistency and asymptotic normality of this renewable estimator under regular conditions. Extensive simulations and real-data experiments demonstrate that our method performs comparably to the oracle estimator while maintaining computational efficiency and low storage requirements.