Optimal subsampling for multiplicative regression with massive data

Abstract

Faced with massive data, subsampling is a popular way to downsize the data volume for reducing computational burden. The key idea of subsampling is to perform statistical analysis on a representative subsample drawn from the full data. It provides a practical solution to extracting useful information from big data. In this article, we develop an efficient subsampling method for large‐scale multiplicative regression model, which can largely reduce the computational burden due to massive data. Under some regularity conditions, we establish consistency and asymptotic normality of the subsample‐based estimator, and derive the optimal subsampling probabilities according to the L‐optimality criterion. A two‐step algorithm is developed to approximate the optimal subsampling procedure. Meanwhile, the convergence rate and asymptotic normality of the two‐step subsample estimator are established. Numerical studies and two real data applications are carried out to evaluate the performance of our subsampling method.