Open Access
April 2012 Two sample tests for high-dimensional covariance matrices
Jun Li, Song Xi Chen
Ann. Statist. 40(2): 908-940 (April 2012). DOI: 10.1214/12-AOS993


We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance–covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample sizes, namely the “large $p$, small $n$” situations and (ii) without assuming parametric distributions for the two populations. These two aspects surpass the capability of the conventional likelihood ratio test. The proposed tests can be used to test on covariances associated with gene ontology terms.


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Jun Li. Song Xi Chen. "Two sample tests for high-dimensional covariance matrices." Ann. Statist. 40 (2) 908 - 940, April 2012.


Published: April 2012
First available in Project Euclid: 1 June 2012

zbMATH: 1274.62383
MathSciNet: MR2985938
Digital Object Identifier: 10.1214/12-AOS993

Primary: 62H15
Secondary: 62G10 , 62G20

Keywords: High-dimensional covariance , Large $p$ small $n$ , likelihood ratio test , testing for gene-sets

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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