A new test for sphericity of the covariance matrix for high dimensional data

Authors:
Thomas J. Fisher;Xiaoqian Sun;Colin M. Gallagher
Affiliations:
Department of Mathematics and Statistics, University of Missouri-Kansas City, Kansas City, MO 64110, USA;Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA;Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

In this paper we propose a new test procedure for sphericity of the covariance matrix when the dimensionality, p, exceeds that of the sample size, N=n+1. Under the assumptions that (A) 0~ for i=1,...,16 and (B) p/n-c~. Our simulation results show that the new test is comparable to, and in some cases more powerful than, the tests for sphericity in the current literature.