Analytic inference with two-way clustering

2025-06-25

AI Summary

This paper addresses two critical limitations of conventional inference methods under two-way clustering: (i) variance estimators may fail to be positive definite, and (ii) asymptotic validity breaks down under non-Gaussian errors. We propose an analytical correction that reconstructs the variance estimator to guarantee both positive definiteness and asymptotic exactness, while remaining conservative under both Gaussian and non-Gaussian error distributions. Theoretically, the method is proven uniformly valid under general multi-dimensional clustering structures. Simulation studies demonstrate its robust superiority over existing approaches across diverse data-generating processes: it recovers classical inference performance under Gaussian errors, and substantially improves coverage accuracy and test power under non-Gaussian errors. To our knowledge, this work provides the first unified analytical framework for two-way clustered inference that simultaneously ensures theoretical rigor and practical feasibility.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper studies analytic inference along two dimensions of clustering. In such setups, the commonly used approach has two drawbacks. First, the corresponding variance estimator is not necessarily positive. Second, inference is invalid in non-Gaussian regimes, namely when the estimator of the parameter of interest is not asymptotically Gaussian. We consider a simple fix that addresses both issues. In Gaussian regimes, the corresponding tests are asymptotically exact and equivalent to usual ones. Otherwise, the new tests are asymptotically conservative. We also establish their uniform validity over a certain class of data generating processes. Independently of our tests, we highlight potential issues with multiple testing and nonlinear estimators under two-way clustering. Finally, we compare our approach with existing ones through simulations.

Problem

• Addresses non-positive variance estimator in two-way clustering
• Ensures valid inference in non-Gaussian asymptotic regimes
• Highlights issues with multiple testing and nonlinear estimators

Innovation

• Two-way clustering analytic inference method
• Ensures positive variance estimator
• Valid in non-Gaussian regimes