The limit distribution of the maximum probability nearest neighbor ball
| Autor: | Györfi, László, Henze, Norbert, Walk, Harro |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $X_1, \ldots, X_n$ be independent random points drawn from an absolutely continuous probability measure with density $f$ in $\mathbb{R}^d$. Under mild conditions on $f$, we derive a Poisson limit theorem for the number of large probability nearest neighbor balls. Denoting by $P_n$ the maximum probability measure of nearest neighbor balls, this limit theorem implies a Gumbel extreme value distribution for $nP_n - \ln n$ as $n \to \infty$. Moreover, we derive a tight upper bound on the upper tail of the distribution of $nP_n - \ln n$, which does not depend on $f$. Comment: 20 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|