The Annals of Statistics

Two sample tests for high-dimensional covariance matrices

Jun Li and Song Xi Chen

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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.

Article information

Ann. Statist., Volume 40, Number 2 (2012), 908-940.

First available in Project Euclid: 1 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H15: Hypothesis testing
Secondary: 62G10: Hypothesis testing 62G20: Asymptotic properties

High-dimensional covariance large $p$ small $n$ likelihood ratio test testing for gene-sets


Li, Jun; Chen, Song Xi. Two sample tests for high-dimensional covariance matrices. Ann. Statist. 40 (2012), no. 2, 908--940. doi:10.1214/12-AOS993.

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