Two sample tests for high-dimensional covariance matrices
Jun Li and Song Xi Chen
Source: Ann. Statist. Volume 40, Number 2
(2012), 908-940.
Abstract
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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Keywords: High-dimensional covariance; large $p$ small $n$; likelihood ratio test; testing for gene-sets
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1338515142
Digital Object Identifier: doi:10.1214/12-AOS993
Zentralblatt MATH identifier: 06073780
Mathematical Reviews number (MathSciNet): MR2985938
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