This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and key techniques used to establish those results. We then review selected applications of high-dimensional bootstrap: construction of simultaneous confidence sets for high-dimensional vector parameters, multiple hypothesis testing via step-down, postselection inference, intersection bounds for partially identified parameters, and inference on best policies in policy evaluation. Finally, we also comment on a couple of future research directions.

中文翻译：

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高维数据 Bootstrap


本文综述了高维 Bootstrap 的最新进展。我们首先回顾了样本平均向量在矩形上分布的高维中心极限定理、高维度的 bootstrap 一致性结果以及用于建立这些结果的关键技术。然后，我们回顾了高维 bootstrap 的选定应用：为高维向量参数构建同步置信集、通过降级进行多假设检验、选择后推理、部分识别参数的交集边界以及政策评估中最佳策略的推理。最后，我们还对几个未来的研究方向进行了评论。