Aoshima M, Shen D, Shen H, Yata K, Zhou YH, Marron JS. A survey of high dimension low sample size asymptotics.
AUST NZ J STAT 2018;
60:4-19. [PMID:
30197552 PMCID:
PMC6124695 DOI:
10.1111/anzs.12212]
[Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
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.
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