🤖 AI Summary
This study addresses the challenge of node-level two-sample hypothesis testing in Gaussian graphical models, where existing methods struggle with precise localization on decomposable graphs and exhibit instability under small sample sizes. The authors propose a leave-one-out Bartlett-corrected likelihood ratio test based on fully connected graphs, which enables calibrated significance inference for individual nodes and fixed-size node subsets—a capability not previously achieved. By integrating a leave-one-out strategy with Bartlett correction, the method constructs a test statistic whose null distribution asymptotically follows a standard chi-squared distribution, thereby overcoming limitations inherent in traditional clique-based decomposition approaches. Simulations demonstrate that the proposed test achieves excellent calibration and statistical power, and its practical utility is further corroborated through real-data analysis.
📝 Abstract
We study two-sample equality testing in Gaussian graphical models. Classical likelihood ratio tests on decomposable graphs admit clique-wise factorizations, offering limited localization and unstable finite-sample behaviour. We propose node-level inference via a leave-one-out Bartlett-adjusted test on a fully connected graph. The resulting increments have standard chi-square null limits, enabling calibrated significance for single nodes and fixed-size subsets. Simulations confirm validity, and a case study shows practical utility.