On the supremum and its location of the standardized uniform empirical process
Probability
2025-12-22 v1 Statistics Theory
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2512.17674,
title = {On the supremum and its location of the standardized uniform empirical process},
author = {Dietmar Ferger},
journal= {arXiv preprint arXiv:2512.17674},
year = {2025}
}
Comments
6 pages