Goodness-of-fit tests for high-dimensional Gaussian graphical models via exchangeable sampling

• 成果类型: Article; Early Access
• 署名作者: Lin, Xiaotong; Li, Weihao; Tian, Fangqiao; Huang, Dongming
• 署名单位: National University of Singapore; National University of Singapore
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf032
• 发表日期: 2025
• 关键词: climate-change; selection; matrices

摘要

We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on sufficient statistics. This framework provides exact finite-sample error control regardless of the dimension and allows flexible choices of test statistics to improve power. We explore several candidate test statistics and conduct extensive simulation studies to demonstrate their finite-sample performance compared to existing methods. The proposed tests exhibit superior power, particularly in cases where the true precision matrix deviates from the null hypothesis due to many small nonzero entries. To justify theoretically, we consider a high-dimensional setting where the proposed test achieves rate-optimality under two distinct signal patterns in the precision matrix: (1) dense patterns with many small nonzero entries and (2) strong patterns with at least one large entry. Finally, we illustrate the usefulness of the proposed test through real-world applications.