Document Zbl 1274.62383

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Stat.</a> <a href="/?q=in%3A305689" title="Articles in this Issue">40, No. 2, 908-940 (2012)</a>. </div> <div class="abstract">Summary: 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.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A6073780">Cited in <strong>2</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A6073780">Cited in <strong>109</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62H15" title="MSC2020">62H15</a> </td> <td class="space"> Hypothesis testing in multivariate analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G10" title="MSC2020">62G10</a> </td> <td class="space"> Nonparametric hypothesis testing </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G20" title="MSC2020">62G20</a> </td> <td class="space"> Asymptotic properties of nonparametric inference </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ahigh-dimensional+covariance">high-dimensional covariance</a>; <a href="/?q=ut%3Alarge+%5C%28p%5C%29%2C+small+%5C%28n%5C%29">large $p$, small $n$</a>; <a href="/?q=ut%3Alikelihood+ratio+test">likelihood ratio test</a>; <a href="/?q=ut%3Atesting+for+gene-sets">testing for gene-sets</a></div> <div class="software"> <h3>Software:</h3><a href="/software/18747">GSA</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1274.62383" data-ciurl="/ci/06073780" data-biburl="/bibtex/06073780.bib" data-amsurl="/amsrefs/06073780.bib" data-xmlurl="/xml/06073780.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06073780.pdf" title="Zbl 1274.62383 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1214/12-AOS993" aria-label="DOI for “Two sample tests for high-dimensional covariance matrices”" title="10.1214/12-AOS993">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1206.0917"title="Note: arXiv document may differ from published version">arXiv</a> <a class="btn btn-default btn-xs" type="button" href="https://projecteuclid.org/euclid.aos/1338515142" title="Full Text at Project Euclid">Euclid</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Anderson, T. 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