Peter Hall's work illuminated many aspects of statistical thought, some of which are very well known including the bootstrap and smoothing. However, he also explored many other lesser known aspects of mathematical statistics. This is a survey of one of those areas, initiated by a seminal paper in 2005, on high dimension low sample size asymptotics. An interesting characteristic of that first paper, and of many of the following papers, is that they contain deep and insightful concepts which are frequently surprising and counter-intuitive, yet have mathematical underpinnings which tend to be direct and not difficult to prove.

中文翻译：

---

高维低样本量渐近的调查

Peter Hall 的工作阐明了统计思想的许多方面，其中一些非常有名，包括引导和平滑。然而，他还探索了数理统计的许多其他鲜为人知的方面。这是对其中一个领域的调查，由 2005 年一篇关于高维低样本量渐近的开创性论文发起。第一篇论文以及随后的许多论文的一个有趣特征是，它们包含深刻而有见地的概念，这些概念经常令人惊讶和违反直觉，但具有倾向于直接且不难证明的数学基础。