A survey of high dimension low sample size asymptotics. (14th March 2018)

• Record Type: Journal Article
• Authors: Aoshima, Makoto; Shen, Dan; Shen, Haipeng; Yata, Kazuyoshi; Zhou, Yi‐Hui; Marron, J. S.
• Is Part Of: Australian & New Zealand journal of statistics. Volume 60:Number 1(2018)
• Page Start: 4
• Page End: 19
• Publication Date: 2018-03-14
• Subjects: canonical correlations -- classification -- geometric representation -- hypothesis testing -- principal component analysis; Statistics -- Periodicals; 519.5
• DOI: 10.1111/anzs.12212
• Languages: English
• ISSNs: 1369-1473

Abstract

Summary: 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. Abstract : This is a survey of HDLSS asymptotics. We introduce geometric representations, classical PCA, new PCAs, classifications and hypothesis tests in HDLSS settings