高维小样本渐近性研究
A survey of high dimension low sample size asymptotics.
作者信息
Aoshima Makoto, Shen Dan, Shen Haipeng, Yata Kazuyoshi, Zhou Yi-Hui, Marron J S
机构信息
Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan.
Interdisciplinary Data Sciences Consortium, Department of Mathematics & Statistics, University of South Florida, FL 33620, USA.
出版信息
Aust N Z J Stat. 2018 Mar;60(1):4-19. doi: 10.1111/anzs.12212. Epub 2018 Mar 14.
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.
彼得·霍尔的工作阐明了统计思想的许多方面，其中一些非常著名，包括自助法和光滑法。然而，他也探索了数理统计学中许多其他鲜为人知的方面。本文是对其中一个领域的综述，该领域由2005年一篇具有开创性的论文发起，涉及高维低样本量渐近性。第一篇论文以及许多后续论文的一个有趣特点是，它们包含深刻而有见地的概念，这些概念常常令人惊讶且有悖直觉，但却有直接且不难证明的数学基础。
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