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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.05818 |
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| _version_ | 1866913979825127424 |
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| author | Gui, Lin Mao, Tiantian Wang, Jingshu Wang, Ruodu |
| author_facet | Gui, Lin Mao, Tiantian Wang, Jingshu Wang, Ruodu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence Gui, Lin Mao, Tiantian Wang, Jingshu Wang, Ruodu Statistics Theory 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. |
| title | Validity and Power of Heavy-Tailed Combination Tests under Asymptotic Dependence |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2508.05818 |