Post-Hoc Large-Sample Statistical Inference
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917324314902528 |
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| author | Chugg, Ben Gauthier, Etienne Jordan, Michael I. Ramdas, Aaditya Waudby-Smith, Ian |
| author_facet | Chugg, Ben Gauthier, Etienne Jordan, Michael I. Ramdas, Aaditya Waudby-Smith, Ian |
| contents | We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error" -- is selected prior to seeing or analyzing any data. This restriction leads to some drawbacks. For instance, if an analyst generates an inconclusive confidence interval, repeating the process with a larger significance level is not an option -- the result is final. Recently, e-values have emerged as the solution to this problem, being both necessary and sufficient tools for performing various forms of post-hoc inference. All such results, however, have thus far been nonasymptotic. As a result, they inherit familiar limitations of nonasymptotic inferential procedures such as requiring strong moment assumptions and being conservative in general. This paper develops a theory of post-hoc inference in the asymptotic setting, yielding asymptotic post-hoc confidence sets and asymptotic post-hoc p-values that make weaker assumptions and are sharper than their nonasymptotic counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08002 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Post-Hoc Large-Sample Statistical Inference Chugg, Ben Gauthier, Etienne Jordan, Michael I. Ramdas, Aaditya Waudby-Smith, Ian Statistics Theory Methodology We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error" -- is selected prior to seeing or analyzing any data. This restriction leads to some drawbacks. For instance, if an analyst generates an inconclusive confidence interval, repeating the process with a larger significance level is not an option -- the result is final. Recently, e-values have emerged as the solution to this problem, being both necessary and sufficient tools for performing various forms of post-hoc inference. All such results, however, have thus far been nonasymptotic. As a result, they inherit familiar limitations of nonasymptotic inferential procedures such as requiring strong moment assumptions and being conservative in general. This paper develops a theory of post-hoc inference in the asymptotic setting, yielding asymptotic post-hoc confidence sets and asymptotic post-hoc p-values that make weaker assumptions and are sharper than their nonasymptotic counterparts. |
| title | Post-Hoc Large-Sample Statistical Inference |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2603.08002 |