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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高维数据引导

本文回顾了高维引导的最新进展。我们首先回顾矩形上样本均值向量分布的高维中心极限定理、高维中的自举一致性结果以及用于建立这些结果的关键技术。然后，我们回顾了高维引导程序的选定应用：高维向量参数的同时置信集的构建、通过逐步下降的多重假设检验、选择后推理、部分识别参数的交集界限以及政策评估中最佳政策的推理。最后，我们还评论了一些未来的研究方向。