Document Zbl 07523349

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Inst. Stat. Math.</a> <a href="/?q=in%3A481420" title="Articles in this Issue">74, No. 3, 539-557 (2022)</a>. </div> <div class="abstract">Summary: Let $f_{Y|X,Z}(y|x,z)$ be the conditional probability function of $Y$ given $(X, Z)$, where $Y$ is the scalar response variable, while $(X, Z)$ is the covariable vector. This paper proposes a robust model selection criterion for $f_{Y|X,Z}(y|x,z)$ with $X$ missing at random. The proposed method is developed based on a set of assumed models for the selection probability function. However, the consistency of model selection by our proposal does not require these models to be correctly specified, while it only requires that the selection probability function is a function of these assumed selective probability functions. Under some conditions, it is proved that the model selection by the proposed method is consistent and the estimator for population parameter vector is consistent and asymptotically normal. A Monte Carlo study was conducted to evaluate the finite-sample performance of our proposal. A real data analysis was used to illustrate the practical application of our proposal.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7523349">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%3Amodel+selection">model selection</a>; <a href="/?q=ut%3Ainverse+probability+weight">inverse probability weight</a>; <a href="/?q=ut%3Amodel+misspecification">model misspecification</a>; <a href="/?q=ut%3Amissing+at+random">missing at random</a>; <a href="/?q=ut%3AKullback-Leibler+divergence">Kullback-Leibler divergence</a>; <a href="/?q=ut%3Arobust">robust</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 07523349" data-ciurl="/ci/07523349" data-biburl="/bibtex/07523349.bib" data-amsurl="/amsrefs/07523349.bib" data-xmlurl="/xml/07523349.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07523349.pdf" title="Zbl 07523349 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/s10463-021-00806-2" aria-label="DOI for “Robust model selection with covariables missing at random”" title="10.1007/s10463-021-00806-2">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">Celeux, G.; Forbes, F.; Robert, CP; Titterington, DM, Deviance information criteria for missing data models, Bayesian Analysis, 1, 4, 651-673 (2006) · <a href="/1331.62329" class="nowrap">Zbl 1331.62329</a></td> </tr><tr> <td>[2]</td> <td class="space">Claeskens, G.; Consentino, F., Variable selection with incomplete covariate data, Biometrics, 64, 4, 1062-1069 (2008) · <a href="/1152.62388" class="nowrap">Zbl 1152.62388</a> · <a href="https://doi.org/10.1111/j.1541-0420.2008.01003.x" class="nowrap">doi:10.1111/j.1541-0420.2008.01003.x</a></td> </tr><tr> <td>[3]</td> <td class="space">Claeskens, G.; Hjort, NL, The focused information criterion, Journal of the American Statistical Association, 98, 464, 900-916 (2003) · <a href="/1045.62003" class="nowrap">Zbl 1045.62003</a> · <a href="https://doi.org/10.1198/016214503000000819" class="nowrap">doi:10.1198/016214503000000819</a></td> </tr><tr> <td>[4]</td> <td class="space">Claeskens, G.; Hjort, NL, Model selection and model averaging (2008), Cambridge University Press · <a href="/1166.62001" class="nowrap">Zbl 1166.62001</a></td> </tr><tr> <td>[5]</td> <td class="space">Fang, F.; Shao, J., Model selection with nonignorable nonresponse, Biometrika, 103, 4, 861-874 (2016) · <a href="https://doi.org/10.1093/biomet/asw039" class="nowrap">doi:10.1093/biomet/asw039</a></td> </tr><tr> <td>[6]</td> <td class="space">Gelman, A., Van Mechelen, I., Verbeke, G., Heitjan, D. 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This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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