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Sin.</a> <a href="/?q=in%3A504487" title="Articles in this Issue">33, No. 4, 2463-2493 (2023)</a>. </div> <div class="abstract">Summary: Multinomial logistic regression models are popular in multicategory classification analysis, but existing models suffer several intrinsic drawbacks. In particular, the parameters cannot be determined uniquely because of the over-specification. Although additional constraints have been imposed to refine the model, such mod- ifications can be inefficient and complicated. In this paper, we propose a novel and efficient simplex-based multinomial logistic regression technique, seamlessly connecting binomial and multinomial cases under a unified framework. Compared with existing models, our model has fewer parameters, is free of any constraints, and can be solved efficiently using the Fisher scoring algorithm. In addition, the proposed model enjoys several theoretical advantages, including Fisher consistency and sharp comparison inequality. Under mild conditions, we establish the asymptotical normality and convergence for the new model, even when the numbers of categories and covariates increase with the sample size. The proposed framework is illustrated by means of extensive simulations and real applications.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7764892">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%3Aasymptotics">asymptotics</a>; <a href="/?q=ut%3Aclassification">classification</a>; <a href="/?q=ut%3AFisher+consistency">Fisher consistency</a>; <a href="/?q=ut%3Akernel+learning">kernel learning</a>; <a href="/?q=ut%3AMLR">MLR</a>; <a href="/?q=ut%3Asimplex+coding+scheme">simplex coding scheme</a></div> <div class="software"> <h3>Software:</h3><a href="/software/11049">ElemStatLearn</a>; <a href="/software/771">R</a>; <a href="/software/21105">ImageNet</a>; <a href="/software/8159">glmnet</a>; <a href="/software/11003">aplore3</a>; <a href="/software/27750">catdata</a>; <a href="/software/18444">VGAMdata</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07764892" data-ciurl="/ci/07764892" data-biburl="/bibtex/07764892.bib" data-amsurl="/amsrefs/07764892.bib" data-xmlurl="/xml/07764892.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07764892.pdf" title="Zbl 07764892 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/10.5705/ss.202021.0082" aria-label="DOI for “Simplex-based multinomial logistic regression with diverging numbers of categories and covariates”" title="10.5705/ss.202021.0082">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">Albert, A. and Anderson, J. 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