Document Zbl 07702553

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Stat., Theory Methods</a> <a href="/?q=in%3A498515" title="Articles in this Issue">52, No. 9, 3108-3123 (2023)</a>. </div> <div class="abstract">Summary: This paper is concerned with comparison problems of predictors between a linear mixed model (LMM) that includes both fixed and random effects and its transformed model under general assumptions. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of unknown vectors under the models by using various inertia and rank formulas of block matrices. We also give some results for special transformed models such as submodels of original LMMs by applying the results obtained for general cases.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7702553">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62J05" title="MSC2020">62J05</a> </td> <td class="space"> Linear regression; mixed models </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62H12" title="MSC2020">62H12</a> </td> <td class="space"> Estimation in multivariate analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A15A03" title="MSC2020">15A03</a> </td> <td class="space"> Vector spaces, linear dependence, rank, lineability </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ABLUP">BLUP</a>; <a href="/?q=ut%3Acovariance+matrix">covariance matrix</a>; <a href="/?q=ut%3Ainertia">inertia</a>; <a href="/?q=ut%3Alinear+mixed+model">linear mixed model</a>; <a href="/?q=ut%3Arank">rank</a>; <a href="/?q=ut%3Atransformed+model">transformed model</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 07702553" data-ciurl="/ci/07702553" data-biburl="/bibtex/07702553.bib" data-amsurl="/amsrefs/07702553.bib" data-xmlurl="/xml/07702553.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07702553.pdf" title="Zbl 07702553 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/10.1080/03610926.2021.1967397" aria-label="DOI for “Inertia and rank approach in transformed linear mixed models for comparison of BLUPs”" title="10.1080/03610926.2021.1967397">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Alalouf, I. 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