Document Zbl 1471.62338

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Stat.</a> <a href="/?q=in%3A456132" title="Articles in this Issue">48, No. 4, 2303-2322 (2020)</a>. </div> <div class="abstract">The paper under review deals with the problem of separability. The authors review the existing tools for validating the assumption of separability for surface data (which is often made in situations where the covariance structure cannot be easily estimated) and, using a setup similar to [<span class="zbmathjax-textit">J. A. D. Aston</span> et al., Ann. Stat. 45, No. 4, 1431–1461 (2017; <a href="/1407.62147">Zbl 1407.62147</a>)], present an alternative test for the hypothesis of separability in hypersurface data. They derive an explicit expression for the minimal distance between the covariance operator and its approximation by a separable covariance operator (it turns out that this minimum vanishes if and only if the covariance operator is separable) and directly estimate the minimal distance (and not the covariance operator itself) from the available data. As a consequence the calculation of the test statistic does neither use an estimate of the full nonseparable covariance operator nor requires the specification of subspaces used for a projection. The authors also prove the consistency of the proposed estimator of the minimum distance and derive its asymptotic distribution under the null hypothesis & alternative. These results are used to develop an asymptotic and a bootstrap test for the hypothesis of separability, which are consistent against all alternatives. Next, an investigation of the finite sample properties of the new tests (by means of a simulation study) and a comparison with some existing alternative tests for this problem are conducted.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A2384">Joseph Melamed (Los Angeles)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7285295">Cited in <strong>7</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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><tr> <td> <a class="mono" href="/classification/?q=cc%3A62R10" title="MSC2020">62R10</a> </td> <td class="space"> Functional data analysis </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Afunctional+data">functional data</a>; <a href="/?q=ut%3Aminimum+distance">minimum distance</a>; <a href="/?q=ut%3Aseparability">separability</a>; <a href="/?q=ut%3Aspace-time+processes">space-time processes</a>; <a href="/?q=ut%3Asurface+data+structures">surface data structures</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1407.62147">Zbl 1407.62147</a></div> <div class="software"> <h3>Software:</h3><a href="/software/36419">covsep</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 1471.62338" data-ciurl="/ci/07285295" data-biburl="/bibtex/07285295.bib" data-amsurl="/amsrefs/07285295.bib" data-xmlurl="/xml/07285295.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07285295.pdf" title="Zbl 1471.62338 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/10.1214/19-AOS1888" aria-label="DOI for “A test for separability in covariance operators of random surfaces”" title="10.1214/19-AOS1888">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1710.08388"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/1597370674" 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">Aston, J. 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