Algorithmic subsampling under multiway clustering

TL;DR

This paper introduces a new algorithmic subsampling method for multiway clustered data, establishing theoretical properties and demonstrating improved inference accuracy and robustness against degeneracy.

Contribution

It develops novel asymptotic theories for multiway algorithmic subsampling, including a uniform weak law of large numbers and a central limit theorem, with practical applications.

Findings

Enhanced robustness against degeneracy in asymptotic distributions

Simulation results show increased inference accuracy

Theoretical proofs of consistency and asymptotic normality

Abstract

This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for the multiway algorithmic subsample means. Consequently, we discover an additional advantage of the algorithmic subsampling that it allows for robustness against potential degeneracy, and even non-Gaussian degeneracy, of the asymptotic distribution under multiway clustering. Simulation studies support this novel result, and demonstrate that inference with the algorithmic subsampling entails more accuracy than that without the algorithmic subsampling. Applying these basic asymptotic theories, we derive the consistency and the asymptotic normality for the multiway algorithmic subsampling generalized method of moments estimator and for the multiway algorithmic subsampling M-estimator. We illustrate an application to scanner data.