On the supremum and its location of the standardized uniform empirical process
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917157365874688 |
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| author | Ferger, Dietmar |
| author_facet | Ferger, Dietmar |
| contents | We show that the maximizing point and the supremum of the standardized uniform empirical process converge in distribution. Here, the limit variable (Z, Y ) has independent components. Moreover, Z attains the values zero and one with equal probability one half and Y follows the Gumbel-distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the supremum and its location of the standardized uniform empirical process Ferger, Dietmar Probability Statistics Theory We show that the maximizing point and the supremum of the standardized uniform empirical process converge in distribution. Here, the limit variable (Z, Y ) has independent components. Moreover, Z attains the values zero and one with equal probability one half and Y follows the Gumbel-distribution. |
| title | On the supremum and its location of the standardized uniform empirical process |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2512.17674 |