On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929218464514048 |
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| author | Park, Jinyoung Pham, Huy Tuan |
| author_facet | Park, Jinyoung Pham, Huy Tuan |
| contents | For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-$p$ setting, and answer a question of Talagrand on the analogous result for general positive empirical processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_10309 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes Park, Jinyoung Pham, Huy Tuan Probability Discrete Mathematics Combinatorics (Primary) 60G70, 60E15, (Secondary) 60C05, 60G15, 60G17 For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-$p$ setting, and answer a question of Talagrand on the analogous result for general positive empirical processes. |
| title | On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes |
| topic | Probability Discrete Mathematics Combinatorics (Primary) 60G70, 60E15, (Secondary) 60C05, 60G15, 60G17 |
| url | https://arxiv.org/abs/2204.10309 |