Mosaic inference on panel data

2025-06-04

AI Summary

Panel data linear regression commonly assumes joint independence across clusters, yet this assumption is frequently violated in practice, leading to invalid standard inference. To address this, we propose the mosaic permutation test—a residual-based resampling method that replaces the strong cluster independence assumption with a weaker “local exchangeability” condition, ensuring valid finite-sample statistical inference while remaining compatible with conventional settings. Our approach constructs robust confidence intervals and conducts hypothesis tests via residual reconstruction and localized permutations. Empirical evaluations on multiple canonical datasets reveal that prevailing methods exhibit variance estimation bias up to fivefold; in contrast, our method substantially improves calibration and robustness, thereby enhancing inferential reliability. The implementation is publicly available as an open-source Python package, *mosaicperm*.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Causality

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Analysis of panel data via linear regression is widespread across disciplines. To perform statistical inference, such analyses typically assume that clusters of observations are jointly independent. For example, one might assume that observations in New York are independent of observations in New Jersey. Are such assumptions plausible? Might there be hidden dependencies between nearby clusters? This paper introduces a mosaic permutation test that can (i) test the cluster-independence assumption and (ii) produce confidence intervals for linear models without assuming the full cluster-independence assumption. The key idea behind our method is to apply a permutation test to carefully constructed residual estimates that obey the same invariances as the true errors. As a result, our method yields finite-sample valid inferences under a mild"local exchangeability"condition. This condition differs from the typical cluster-independence assumption, as neither assumption implies the other. Furthermore, our method is asymptotically valid under cluster-independence (with no exchangeability assumptions). Together, these results show our method is valid under assumptions that are arguably weaker than the assumptions underlying many classical methods. In experiments on well-studied datasets from the literature, we find that many existing methods produce variance estimates that are up to five times too small, whereas mosaic methods produce reliable results. We implement our methods in the python package mosaicperm.

Problem

• Testing cluster-independence assumption in panel data analysis
• Producing confidence intervals without full cluster-independence
• Validating inferences under weaker local exchangeability conditions

Innovation

• Mosaic permutation test for cluster-independence
• Local exchangeability condition for valid inferences
• Python package mosaicperm implements the method