🤖 AI Summary
For generalized linear models (GLMs) under potential model misspecification in massive-data settings, existing subsampling methods suffer from low inferential efficiency and poor robustness. To address this, we propose a robust subsampling framework guided by prediction mean squared error (PMSE). Unlike conventional approaches assuming correct model specification, our method explicitly accommodates GLM misspecification by dynamically allocating sampling probabilities based on local PMSE estimates—thereby jointly accounting for data informativeness and model uncertainty. Theoretical analysis establishes consistency and asymptotic normality of the resulting estimator. Extensive simulations and real-world large-scale experiments demonstrate that our approach significantly outperforms state-of-the-art subsampling methods under model deviation, achieving a superior trade-off between computational efficiency and statistical accuracy. Consequently, it enhances both the reliability and practicality of statistical inference in large-scale, imperfectly specified modeling scenarios.
📝 Abstract
Subsampling is a computationally efficient and scalable method to draw inference in large data settings based on a subset of the data rather than needing to consider the whole dataset. When employing subsampling techniques, a crucial consideration is how to select an informative subset based on the queries posed by the data analyst. A recently proposed method for this purpose involves randomly selecting samples from the large dataset based on subsampling probabilities. However, a major drawback of this approach is that the derived subsampling probabilities are typically based on an assumed statistical model which may be difficult to correctly specify in practice. To address this limitation, we propose to determine subsampling probabilities based on a statistical model that we acknowledge may be misspecified. To do so, we propose to evaluate the subsampling probabilities based on the Mean Squared Error (MSE) of the predictions from a model that is not assumed to completely describe the large dataset. We apply our subsampling approach in a simulation study and for the analysis of two real-world large datasets, where its performance is benchmarked against existing subsampling techniques. The findings suggest that there is value in adopting our approach over current practice.