Renewable Learning for Multiplicative Regression with Streaming Datasets

When large amounts of data continuously arrive in streams, online updating is an effective way to reduce storage and computational burden. The key idea of online updating is that the previous estimators are sequentially updated only using the current data and some summary statistics of historical raw data. In this article, we develop a renewable learning method for a multiplicative regression model with streaming data, where the parameter estimator based on a least product relative error criterion is renewed without revisiting any historical raw data. Under some regularity conditions, we establish the consistency and asymptotic normality of the renewable estimator. Moreover, the theoretical results confirm that the proposed renewable estimator achieves the same asymptotic distribution as the least product relative error estimator with the entire dataset. Numerical studies and two real data examples are provided to evaluate the performance of our proposed method.