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Journal of Probability and Statistics
Volume 2012, Article ID 728565, 18 pages
http://dx.doi.org/10.1155/2012/728565
Research Article

-Plot for Testing Spherical Symmetry for High-Dimensional Data with a Small Sample Size

College of Business, University of New Haven, 300 Boston Post Road, West Haven, CT 06516, USA

Received 3 August 2012; Accepted 16 October 2012

Academic Editor: Jose Sarabia

Copyright © 2012 Jiajuan Liang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

High-dimensional data with a small sample size, such as microarray data and image data, are commonly encountered in some practical problems for which many variables have to be measured but it is too costly or time consuming to repeat the measurements for many times. Analysis of this kind of data poses a great challenge for statisticians. In this paper, we develop a new graphical method for testing spherical symmetry that is especially suitable for high-dimensional data with small sample size. The new graphical method associated with the local acceptance regions can provide a quick visual perception on the assumption of spherical symmetry. The performance of the new graphical method is demonstrated by a Monte Carlo study and illustrated by a real data set.