Carefree multiple testing with e-processes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909692252389376 |
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| author | Tavyrikov, Yury Goeman, Jelle J. de Heide, Rianne |
| author_facet | Tavyrikov, Yury Goeman, Jelle J. de Heide, Rianne |
| contents | E-processes enable hypothesis testing with ongoing data collection while maintaining Type I error control. However, when testing multiple hypotheses simultaneously, current $e$-value based multiple testing methods such as e-BH are not invariant to the order in which data are gathered for the different $e$-processes. This can lead to undesirable situations, e.g., where a hypothesis rejected at time $t$ is no longer rejected at time $t+1$ after choosing to gather more data for one or more $e$-processes unrelated to that hypothesis. We argue that multiple testing methods should always work with suprema of $e$-processes. We provide an example to illustrate that e-BH does not control the FDR, at level $α$ when applied to suprema of $e$-processes. From the same example we see that the FWER is not controlled with averaging, and also closed e-BH does not control the FDR. We show that adjusters can be used to ensure FDR-sup control with e-BH under arbitrary dependence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carefree multiple testing with e-processes Tavyrikov, Yury Goeman, Jelle J. de Heide, Rianne Statistics Theory Methodology E-processes enable hypothesis testing with ongoing data collection while maintaining Type I error control. However, when testing multiple hypotheses simultaneously, current $e$-value based multiple testing methods such as e-BH are not invariant to the order in which data are gathered for the different $e$-processes. This can lead to undesirable situations, e.g., where a hypothesis rejected at time $t$ is no longer rejected at time $t+1$ after choosing to gather more data for one or more $e$-processes unrelated to that hypothesis. We argue that multiple testing methods should always work with suprema of $e$-processes. We provide an example to illustrate that e-BH does not control the FDR, at level $α$ when applied to suprema of $e$-processes. From the same example we see that the FWER is not controlled with averaging, and also closed e-BH does not control the FDR. We show that adjusters can be used to ensure FDR-sup control with e-BH under arbitrary dependence. |
| title | Carefree multiple testing with e-processes |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2501.19360 |