Document Zbl 1365.62207

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Pap.</a> <a href="/?q=in%3A366395" title="Articles in this Issue">58, No. 2, 467-484 (2017)</a>. </div> <div class="abstract">Summary: Best linear unbiased estimators (BLUEs) of unknown parameters under linear models have minimum covariance matrices in the Löwner partial ordering among all linear unbiased estimators of the unknown parameters. Hence, BLUEs’ covariance matrices are usually used as a criterion to compare optimality with other types of estimator. During this work, people often need to establish certain equalities and inequalities for BLUEs’ covariance matrices, and use them in statistical inference of regression models. This paper aims at establishing some analytical formulas for calculating ranks and inertias of BLUEs’ covariance matrices under general linear model, and using these formulas in the comparison of covariance matrices of BLUEs with other types of estimator. This is in fact a mathematical work, and some new tools in matrix analysis are essentially utilized.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6736131">Cited in <strong>15</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3A62J05" title="MSC2020">62J05</a> </td> <td class="space"> Linear regression; mixed models </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62J10" title="MSC2020">62J10</a> </td> <td class="space"> Analysis of variance and covariance (ANOVA) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ageneral+linear+model">general linear model</a>; <a href="/?q=ut%3Ablue">blue</a>; <a href="/?q=ut%3Acovariance+matrix">covariance matrix</a>; <a href="/?q=ut%3Arank">rank</a>; <a href="/?q=ut%3Ainertia">inertia</a>; <a href="/?q=ut%3AL%C3%B6wner+partial+ordering">Löwner partial ordering</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 1365.62207" data-ciurl="/ci/06736131" data-biburl="/bibtex/06736131.bib" data-amsurl="/amsrefs/06736131.bib" data-xmlurl="/xml/06736131.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06736131.pdf" title="Zbl 1365.62207 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/10.1007/s00362-015-0707-x" aria-label="DOI for “Some equalities and inequalities for covariance matrices of estimators under linear model”" title="10.1007/s00362-015-0707-x">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 IS, Styan GPH (1979) Characterizations of estimability in the general linear model. 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