On weighted approximations in $D[0, 1]$ with applications to self-normalized partial sum processes
| dc.creator | Csörgő, Miklós | |
| dc.creator | Szyszkowicz, Barbara | |
| dc.creator | Wang, Qiying | |
| dc.date | 2007-11-09 | |
| dc.date.accessioned | 2026-07-07T08:41:50Z | |
| dc.date.available | 2026-07-07T08:41:50Z | |
| dc.description | Let $X, X_1, X_2,...$ be a sequence of non-degenerate i.i.d. random variables with mean zero. The best possible weighted approximations are investigated in $D[0, 1]$ for the partial sum processes $\{S_{[nt]}, 0\le t\le 1\}$, where $S_n=\sum_{j=1}^nX_j$, under the assumption that $X$ belongs to the domain of attraction of the normal law. The conclusions then are used to establish similar results for the sequence of self-normalized partial sum processes $\{S_{[nt]}/V_n, 0\le t\le 1\}$, where $V_n^2=\sum_{j=1}^nX_j^2$. $L_p$ approximations of self-normalized partial sum processes are also discussed. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/0711.1384 | |
| dc.identifier | http://arxiv.org/abs/0711.1384 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141798 | |
| dc.subject | Probability | |
| dc.subject | 60G50, 60F17, 60F25 (Primary); 62E20 (Secondary) | |
| dc.title | On weighted approximations in $D[0, 1]$ with applications to self-normalized partial sum processes | |
| dc.type | text |