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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.01368 |
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| _version_ | 1866915244315508736 |
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| author | Chen, Yuyu Wang, Ruodu Wang, Yuming Zhu, Wenhao |
| author_facet | Chen, Yuyu Wang, Ruodu Wang, Yuming Zhu, Wenhao |
| contents | We obtain several inequalities on the generalized means of dependent p-values. In particular, the weighted harmonic mean of p-values is strictly sub-uniform under several dependence assumptions of p-values, including independence, negative upper orthant dependence, the class of extremal mixture copulas, and some Clayton copulas. Sub-uniformity of the harmonic mean of p-values has an important implication in multiple hypothesis testing: It is statistically invalid (anti-conservative) to merge p-values using the harmonic mean unless a proper threshold or multiplier adjustment is used, and this applies across all significance levels. The required multiplier adjustment on the harmonic mean p-value grows sub-linearly to infinity as the number of p-values increases, and hence there does not exist a constant multiplier that works for any number of p-values, even under independence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sub-uniformity of harmonic mean p-values Chen, Yuyu Wang, Ruodu Wang, Yuming Zhu, Wenhao Statistics Theory We obtain several inequalities on the generalized means of dependent p-values. In particular, the weighted harmonic mean of p-values is strictly sub-uniform under several dependence assumptions of p-values, including independence, negative upper orthant dependence, the class of extremal mixture copulas, and some Clayton copulas. Sub-uniformity of the harmonic mean of p-values has an important implication in multiple hypothesis testing: It is statistically invalid (anti-conservative) to merge p-values using the harmonic mean unless a proper threshold or multiplier adjustment is used, and this applies across all significance levels. The required multiplier adjustment on the harmonic mean p-value grows sub-linearly to infinity as the number of p-values increases, and hence there does not exist a constant multiplier that works for any number of p-values, even under independence. |
| title | Sub-uniformity of harmonic mean p-values |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2405.01368 |