Almost Sure Convergence of Extreme Order Statistics
| dc.creator | Peng, Zuoxiang | |
| dc.creator | Li, Jiaona | |
| dc.creator | Nadarajah, Saralees | |
| dc.date | 2008-10-03 | |
| dc.date.accessioned | 2026-07-07T10:07:26Z | |
| dc.date.available | 2026-07-07T10:07:26Z | |
| dc.description | Let $M_n^{(k)}$ denote the $k$th largest maximum of a sample $(X_1,X_2,...,X_n)$ from parent $X$ with continuous distribution. Assume there exist normalizing constants $a_n>0$, $b_n\in \mathbb{R}$ and a nondegenerate distribution $G$ such that $a_n^{-1}(M_n^{(1)}-b_n)\stackrel{w}{\to}G$. Then for fixed $k\in \mathbb{N}$, the almost sure convergence of \[\frac{1}{D_N}\sum_{n=k}^Nd_n\mathbb{I}\{M_n^{(1)}\le a_nx_1+b_n,M_n^{(2)}\le a_nx_2+b_n,...,M_n^{(k)}\le a_nx_k+b_n\}\] is derived if the positive weight sequence $(d_n)$ with $D_N=\sum_{n=1}^Nd_n$ satisfies conditions provided by Hörmann. | |
| dc.description | Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0810.0579 | |
| dc.identifier | http://arxiv.org/abs/0810.0579 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170635 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62F15 (Primary) 60G70, 60F15 (Secondary) | |
| dc.title | Almost Sure Convergence of Extreme Order Statistics | |
| dc.type | text |