A survey of high dimension low sample size asymptotics

被引：29

作者：

Aoshima, Makoto ^{[1
]}

Shen, Dan ^{[2
]}

Shen, Haipeng ^{[3
]}

Yata, Kazuyoshi ^{[1
]}

Zhou, Yi-Hui ^{[4
]}

Marron, J. S. ^{[5
]}

机构：

[1] Univ Tsukuba, Inst Math, Ibaraki 3058571, Japan

[2] Univ S Florida, Interdisciplinary Data Sci Consortium, Dept Math & Stat, Tampa, FL 33620 USA

[3] Univ Hong Kong, Innovat & Informat Management, Fac Business & Econ, Hong Kong, Hong Kong, Peoples R China

[4] North Carolina State Univ, Dept Biol Sci, Bioinformat Res Ctr, Raleigh, NC 27695 USA

[5] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27514 USA

来源：

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS | 2018年 / 60卷 / 01期

基金：

日本学术振兴会;

关键词：

canonical correlations; classification; geometric representation; hypothesis testing; principal component analysis; PRINCIPAL COMPONENT ANALYSIS; PCA CONSISTENCY; GEOMETRIC REPRESENTATION; HDLSS DISCRIMINATION; COVARIANCE MATRICES; 2-SAMPLE TEST; SPARSE PCA; TESTS; INFERENCE; CLASSIFIERS;

D O I：

10.1111/anzs.12212

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：4 / 19

页数：16

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