Document Zbl 07532184

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Stat., Theory Methods</a> <a href="/?q=in%3A482381" title="Articles in this Issue">50, No. 21, 4997-5012 (2021)</a>. </div> <div class="abstract">Summary: We consider an extended general linear model containing new observations without making any restrictions on correlation of random vectors and any rank assumptions. We give variety of equalities and inequalities in the comparison of covariance matrix of BLUP of new observations with any other unbiased predictors’ covariance matrices by using rank and inertia formulas. We next consider the general linear mixed model under the assumption that the random effects and the random errors can be correlated. Using connection between the general linear mixed model and the extended general linear model, we give some equalities and inequalities for comparing the covariance matrices of BLUP of linear function of fixed and random effects with covariance matrices of any other type of unbiased predictors. We also give results for special cases and for linear function of partial fixed and random effects.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7532184">Cited in <strong>8</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><tr> <td> <a class="mono" href="/classification/?q=cc%3A15A09" title="MSC2020">15A09</a> </td> <td class="space"> Theory of matrix inversion and generalized inverses </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62-XX" title="MSC2020">62-XX</a> </td> <td class="space"> Statistics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ABLUE">BLUE</a>; <a href="/?q=ut%3ABLUP">BLUP</a>; <a href="/?q=ut%3Acovariance+matrix">covariance matrix</a>; <a href="/?q=ut%3Ageneral+linear+model">general linear model</a>; <a href="/?q=ut%3Ageneral+linear+mixed+model">general linear mixed model</a>; <a href="/?q=ut%3Ainertia">inertia</a>; <a href="/?q=ut%3Arank">rank</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 07532184" data-ciurl="/ci/07532184" data-biburl="/bibtex/07532184.bib" data-amsurl="/amsrefs/07532184.bib" data-xmlurl="/xml/07532184.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07532184.pdf" title="Zbl 07532184 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/10.1080/03610926.2019.1599950" aria-label="DOI for “Rank and inertia formulas for covariance matrices of BLUPs in general linear mixed models”" title="10.1080/03610926.2019.1599950">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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