2025/08/07 by Lin Gui, Gui, Lin, Tiantian Mao +5 · 1 citation
Mathematics · #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2508.05818
openalex publication_date 2025/08/07 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
Heavy-tailed combination tests, such as the Cauchy combination test and harmonic mean p-value method, are widely used for testing global null hypotheses by aggregating dependent p-values. Existing theoretical guarantees, however, are largely restricted to the case of asymptotically independent p-values, leaving the behavior of these tests under broader dependence structures poorly understood. We develop a unified framework based on multivariate regularly varying copulas, a flexible class defined by a mild regularity condition on the joint behavior of p-values near zero, that accommodates a wide range of dependence structures. Within this framework, heavy-tailed combination tests are asymptotically valid when the transformation distribution has tail index γ≤ 1, with γ= 1 maximizing power while preserving validity. We further show that combination tests with γ= 1 achieve strictly greater asymptotic power than Bonferroni's method if and only if the p-values are not asymptotically independent and signals are not extremely sparse, with the power advantage growing as dependence strengthens. Bonferroni emerges as the γ→ 0 limit and becomes overly conservative under asymptotic dependence. These results provide theoretical support for using truncated Cauchy or Pareto combination tests, offering a principled approach to enhance power while controlling false positives under complex dependence.