Gaussian Multiplier Bootstrap Procedure for the $k$th Largest Coordinate of High-Dimensional Statistics
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911480551571456 |
|---|---|
| author | Ding, Yixi Li, Qizhai Shi, Yuke Sun, Liuquan Zhang, Luobin |
| author_facet | Ding, Yixi Li, Qizhai Shi, Yuke Sun, Liuquan Zhang, Luobin |
| contents | We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has been studied previously for $k=1$ (i.e., maxima). However, in many applications, a general $k$ ($k\geq 1$) is of great interest. We provide the upper bounds for the errors between Gaussian approximations and Gaussian multiplier approximations. The dimension $p$ is allowed to be larger than the sample size $n$. The effectiveness of the proposed methods is demonstrated via the computer numerical results and a real-world data analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian Multiplier Bootstrap Procedure for the $k$th Largest Coordinate of High-Dimensional Statistics Ding, Yixi Li, Qizhai Shi, Yuke Sun, Liuquan Zhang, Luobin Statistics Theory We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has been studied previously for $k=1$ (i.e., maxima). However, in many applications, a general $k$ ($k\geq 1$) is of great interest. We provide the upper bounds for the errors between Gaussian approximations and Gaussian multiplier approximations. The dimension $p$ is allowed to be larger than the sample size $n$. The effectiveness of the proposed methods is demonstrated via the computer numerical results and a real-world data analysis. |
| title | Gaussian Multiplier Bootstrap Procedure for the $k$th Largest Coordinate of High-Dimensional Statistics |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2508.14400 |