{"ID":2880095,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.14400","arxiv_id":"2508.14400","title":"Gaussian Multiplier Bootstrap Procedure for the $k$th Largest Coordinate of High-Dimensional Statistics","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2508.14400","url_pdf":"https://arxiv.org/pdf/2508.14400v2","authors":"[\"Yixi Ding\",\"Qizhai Li\",\"Yuke Shi\",\"Liuquan Sun\",\"Luobin Zhang\"]","published":"2025-08-20T03:53:20Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}