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Wiley InterScience

Journal of the Royal Statistical Society: Series B (Statistical Methodology)

Journal of the Royal Statistical Society: Series B (Statistical Methodology)

Volume 67 Issue 3, Pages 427 - 444

Published Online: 24 May 2005

© 2010 The Royal Statistical Society and Blackwell Publishing Ltd



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Geometric representation of high dimension, low sample size data
Peter Hall 1 , J. S.,Marron 2 and Amnon Neeman 3
  1 Australian National University, Canberra, Australia
  2 University of North Carolina, Chapel Hill, USA
  3 Australian National University, Canberra, Australia
Correspondence to J. S. Marron, Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260, USA.
E-mail: marron@email.unc.edu
Copyright 2005 Royal Statistical Society
KEYWORDS
Chemometrics • Large dimensional data • Medical images • Microarrays • Multivariate analysis • Non-standard asymptotics

ABSTRACT

Summary. 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 ∞ 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.


[Received April 2004. Revised February 2005]

DIGITAL OBJECT IDENTIFIER (DOI)
10.1111/j.1467-9868.2005.00510.x About DOI

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