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    <div class="main-content"><div class="container"><div class="thirteen columns"><div class="gutter"><h2>The Annals of Statistics</h2><ul class="nav-pills"><li><a href="/info/euclid.aos">Info</a></li><li><a href="/current/euclid.aos">Current issue</a></li><li><a href="/all/euclid.aos">All issues</a></li><li><a href="/search/euclid.aos">Search</a></li></ul><section class="publication-content"><ul class="pager"><div><li><a href="/euclid.aos/1176344135"> &#x2190; Previous article</a></li><li><a href="/euclid.aos/1176344121#toc">TOC</a></li><li><a href="/euclid.aos/1176344137">Next article &#x2192; </a></li></div> </ul><ul class="citation"><li><a href="/euclid.aos">Ann. Statist.</a></li><li> Volume 6, Number 2 (1978), 461-464.</li></ul><h3>Estimating the Dimension of a Model</h3><p class="small"><a class="trigger" href="#author-euclidaos1176344136SchwarzGideon">Gideon Schwarz</a><div class="popover popover-before-after-applied" style="display: none; " id="author-euclidaos1176344136SchwarzGideon"><span role="presentation" class="before"> </span><h5>More by Gideon Schwarz</h5><p>Search this author in:</p><ul><li><a href="https://scholar.google.com/scholar?as_q=&amp;as_epq=&amp;as_oq=&amp;as_eq=&amp;as_occt=any&amp;as_sauthors=Gideon+Schwarz&amp;as_publication=&amp;as_ylo=&amp;as_yhi=&amp;btnG=&amp;hl=en&amp;as_sdt=0%2C33#">Google Scholar</a></li><li><a href="/search_result?type=index&amp;q.a.author=Gideon%20Schwarz">Project Euclid</a></li></ul><span role="presentation" class="after"> </span></div></p><div class="download-buttons box"><p><strong>Full-text: Open access</strong><div class="download-buttons"> <a class="btn btn-primary" href="/download/pdf_1/euclid.aos/1176344136"><i class="icon-pdf"> </i>PDF File (328 KB)</a>       </div></p></div><div class="tab-set"><ul class="nav-tabs"><li><a href="#abstract">Abstract</a></li><li><a href="#info">Article info and citation</a></li><li><a href="/first_page/euclid.aos/1176344136">First page</a></li></ul><div id="abstract" class="abstract"><h4>Abstract</h4><div class="abstract-text"><p>The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.</p></div></div><div id="info"><h4>Article information</h4><p><strong>Source</strong><br/><a href="/euclid.aos">Ann. Statist.</a>  Volume 6, Number 2 (1978), 461-464.</p><p><strong>Dates</strong><br/>First available in Project Euclid:  12 April 2007<br/></p><p><strong>Permanent link to this document</strong><br/>https://projecteuclid.org/euclid.aos/1176344136</p><p><strong>Digital Object Identifier</strong><br/>doi:10.1214/aos/1176344136</p><p><strong>Mathematical Reviews number (MathSciNet)</strong><br/><a href="http://www.ams.org/mathscinet-getitem?mr=468014"> MR468014</a><br/></p><p><strong>Zentralblatt MATH identifier</strong><br/><a href="https://zbmath.org/?q=an:0379.62005">0379.62005</a></p><p><strong>JSTOR</strong><br/><a href="http://links.jstor.org/sici?sici=0090-5364%28197803%296%3A2%3C461%3AETDOAM%3E2%2E0%2ECO%3B2-5&amp;origin=euclid"> links.jstor.org </a></p><p class="subjects"><strong>Subjects</strong><br/> Primary: <a title="Search this subject in&#10;                                  Euclid" href="/search_result?type=index&amp;linkedSearch=1&amp;q.a.subject=62F99">62F99: None of the above, but in this section</a><br/> Secondary: <a title="Search this subject in&#10;                                  Euclid" href="/search_result?type=index&amp;linkedSearch=1&amp;q.a.subject=62J99">62J99: None of the above, but in this section</a></p><p class="keywords"><strong>Keywords</strong><br/><a title="Search this keyword in&#10;                                Euclid" href="/search_result?type=index&amp;q.a.keyword=Dimension&amp;linkedSearch=1">Dimension</a> <a title="Search this keyword in&#10;                                Euclid" href="/search_result?type=index&amp;q.a.keyword=Akaike+information+criterion&amp;linkedSearch=1">Akaike information criterion</a> <a title="Search this keyword in&#10;                                Euclid" href="/search_result?type=index&amp;q.a.keyword=asymptotics&amp;linkedSearch=1">asymptotics</a> </p><h4>Citation</h4><div id="printer-citation"><p><span id="dynamic_citation">Schwarz, Gideon. Estimating the Dimension of a Model. 
 Ann. Statist. 6 (1978), no. 2, 461--464. doi:10.1214/aos/1176344136. https://projecteuclid.org/euclid.aos/1176344136</span></p></div><br/><div id="export" class="modal hide fade" tabindex="-1" role="dialog" aria-labelledby="moreFacets" aria-hidden="true"><div class="modal-header"><a data-dismiss="modal" aria-hidden="true"><i class="icon-remove"> </i></a><h3 id="myModalLabel">Export citation</h3></div><div class="modal-body"><h4>Format:</h4><select id="export-format-select"><option value="bibtex">Text (BibTeX)</option><option value="printer">Text (printer-friendly)</option><option value="ris">RIS (EndNote, ProCite, Reference Manager)</option></select><h4>Delivery Method:</h4><input type="radio" name="delivery" value="browser" checked="true">Download</input>  <input type="radio" name="delivery" value="email">Email</input>  <input type="text" name="modal-address" disabled="true"/><br/><br/><div class="alert alert-error hidden">Please enter a valid email address.</div><div class="alert alert-success hidden">Email sent.</div></div><div class="modal-footer"><button id="export-button" class="btn btn-primary"><i class="icon-share"> </i> Export</button><button class="btn" data-dismiss="modal" aria-hidden="true">Cancel</button></div></div><form id="export-form" method="post" action="/export_citations" enctype="application/x-www-form-urlencoded"><input id="export-format" name="format" value="bibtex" type="hidden"/><input id="export-delivery" name="delivery" value="browser" type="hidden"/><input id="export-address" name="address" type="hidden"/><input name="h" class="item_toggle" type="hidden" checked="checked" id="euclid.aos/1176344136" value="euclid.aos/1176344136"/><a class="btn export-link-special" href="#export" data-toggle="modal"><i class="icon-share"> </i> Export citation</a></form></div></div></section></div></div><div class="three columns sidebar"><div class="gutter"><div class="publisher-logo"><a href="/publisher/euclid.publisher.ims"><img src="/publisher/images/publisher_ims.png"/></a></div><div class="sidebar-box publisher-nav"><h4><a href="/publisher/euclid.publisher.ims">The Institute of Mathematical Statistics</a></h4><ul><li><a href="http://www.imstat.org/aos/">Editorial Board</a></li><li><a href="http://www.imstat.org/aos/manprep.html">For Authors</a></li><li><a href="http://www.imstat.org/publications/subscriptions.htm">Subscriptions</a></li></ul><ul><li><a href="/firstOnline/euclid.aos">First Online</a></li><li><a href="http://www.imstat.org/aos/future_papers.html">Accepted Papers</a></li></ul></div><div class="sidebar-box sidebar-cover"><img class="border-gray" src="/publication/euclid.aos/images/cover_aos_111.gif" alt="The Annals of Statistics"/></div><div class="sidebar-box journal-tracking"><h3>New content alerts</h3><a href="/login?returnArgs=addEmailToc#myeuclid" class="btn"><i class="icon-envelope"> </i>
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