  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.
