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Geometric representation of high dimension, low sample size data

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  • Peter Hall
  • J. S. Marron
  • Amnon Neeman

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.

Suggested Citation

  • Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:3:p:427-444
    DOI: 10.1111/j.1467-9868.2005.00510.x
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