A Subsampling Strategy for AIC-based Model Averaging with Generalized Linear Models

Subsampling is an effective approach to address computational challenges associated with massive datasets. However, existing subsampling methods do not consider model uncertainty. In this article, we investigate the subsampling technique for the Akaike information criterion (AIC) and extend the subsampling method to the smoothed AIC model-averaging framework in the context of generalized linear models. By correcting the asymptotic bias of the maximized subsample objective function used to approximate the Kullback–Leibler divergence, we derive the form of the AIC based on the subsample. We then provide a subsampling strategy for the smoothed AIC model-averaging estimator and study the corresponding asymptotic properties of the loss and the resulting estimator. A practically implementable algorithm is developed, and its performance is evaluated through numerical experiments on both real and simulated datasets.