Geometric representation of high dimension, low sample size data

被引：296
|
作者：
Hall, P
Marron, JS [1 ]
Neeman, A
机构：
[1] Univ N Carolina, Dept Stat, Chapel Hill, NC 27599 USA
[2] Australian Natl Univ, Canberra, ACT, Australia
来源：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY | 2005年 / 67卷
关键词：
chemometrics; large dimensional data; medical images; microarrays; multivariate analysis; non-standard asymptotics;
D O I：
10.1111/j.1467-9868.2005.00510.x
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：
High dimension, low sample size data are emerging in various areas of science. We find a common structure underlying many such data sets by using a non-standard type of asymptotics: the dimension tends to infinity while the sample size is fixed. Our analysis shows a tendency for the data to lie deterministically at the vertices of a regular simplex. Essentially all the randomness in the data appears only as a random rotation of this simplex. This geometric representation is used to obtain several new statistical insights.
引用
收藏
页码：427 / 444
页数：18
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