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Two sample tests for high-dimensional covariance matrices
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 , small " 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.Comment: Published in at http://dx.doi.org/10.1214/12-AOS993 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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