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A survey of high dimension low sample size asymptotics
Author(s) -
Aoshima Makoto,
Shen Dan,
Shen Haipeng,
Yata Kazuyoshi,
Zhou YiHui,
Marron J. S.
Publication year - 2018
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12212
Subject(s) - mathematics , dimension (graph theory) , smoothing , sample size determination , sample (material) , mathematical statistics , survey sampling , statistics , large sample , econometrics , calculus (dental) , mathematical economics , statistical physics , pure mathematics , sociology , demography , physics , medicine , population , chemistry , dentistry , chromatography
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.