Weighted Asymptotically Optimal Sequential Testing
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911462213025792 |
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| author | Bose, Soumyabrata Bartroff, Jay |
| author_facet | Bose, Soumyabrata Bartroff, Jay |
| contents | This paper develops a framework for incorporating prior information into sequential multiple testing procedures while maintaining asymptotic optimality. We define a weighted log-likelihood ratio (WLLR) as an additive modification of the standard LLR and use it to construct two new sequential tests: the Weighted Gap and Weighted Gap-Intersection procedures. We prove that both procedures provide strong control of the family-wise error rate. Our main theoretical contribution is to show that these weighted procedures are asymptotically optimal; their expected stopping times achieve the theoretical lower bound as the error probabilities vanish. This first-order optimality is shown to be robust, holding in high-dimensional regimes where the number of null hypotheses grows and in settings with random weights, provided that mild, interpretable conditions on the weight distribution are met. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Asymptotically Optimal Sequential Testing Bose, Soumyabrata Bartroff, Jay Methodology This paper develops a framework for incorporating prior information into sequential multiple testing procedures while maintaining asymptotic optimality. We define a weighted log-likelihood ratio (WLLR) as an additive modification of the standard LLR and use it to construct two new sequential tests: the Weighted Gap and Weighted Gap-Intersection procedures. We prove that both procedures provide strong control of the family-wise error rate. Our main theoretical contribution is to show that these weighted procedures are asymptotically optimal; their expected stopping times achieve the theoretical lower bound as the error probabilities vanish. This first-order optimality is shown to be robust, holding in high-dimensional regimes where the number of null hypotheses grows and in settings with random weights, provided that mild, interpretable conditions on the weight distribution are met. |
| title | Weighted Asymptotically Optimal Sequential Testing |
| topic | Methodology |
| url | https://arxiv.org/abs/2511.07588 |