{"ID":2885419,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.05818","arxiv_id":"2508.05818","title":"Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence","abstract":"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. However, their theoretical guarantees under general dependence structures remain limited. We develop a unified framework using multivariate regularly varying copulas to model the joint behavior of p-values near zero. Within this framework, we show that combination tests remain asymptotically valid when the transformation distribution has a tail index $γ\\leq 1$, with $γ= 1$ maximizing power while preserving validity. The Bonferroni test emerges as a limiting case when $γ\\to 0$ and becomes overly conservative under asymptotic dependence. Consequently, combination tests with $γ= 1$ achieve increasing asymptotic power gains over Bonferroni as p-values exhibit stronger lower-tail dependence and signals are not extremely sparse. Our 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.","short_abstract":"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. However, their theoretical guarantees under general dependence structures remain limited. We develop a unified framework using multi...","url_abs":"https://arxiv.org/abs/2508.05818","url_pdf":"https://arxiv.org/pdf/2508.05818v1","authors":"[\"Lin Gui\",\"Tiantian Mao\",\"Jingshu Wang\",\"Ruodu Wang\"]","published":"2025-08-07T19:41:12Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}