Document Zbl 07901853

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Sin.</a> <a href="/?q=in%3A516411" title="Articles in this Issue">34, No. 3, 1545-1564 (2024)</a>. </div> <div class="abstract">Summary: A central topic in functional data analysis is how to design an optimal decision rule, based on training samples, to classify a data function. We exploit the optimal classification problem in which the data functions are Gaussian processes. We derive sharp convergence rates for the minimax excess misclassification risk both when the data functions are fully observed and when they are discretely observed. We explore two easily implementable classifiers, based on a discriminant analysis and on a deep neural network, respectively, which both achieve optimality in Gaussian settings. Our deep neural network classifier is new in the literature, and demonstrates outstanding performance, even when the data functions are nonGaussian. For discretely observed data, we discover a novel critical sampling frequency that governs the sharp convergence rates. The proposed classifiers perform favorably in finite-sample applications, shown in comparisons with otherfunctional classifiers in simulations and one real-data application.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7901853">Cited in <strong>2</strong> Documents</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%3Afunctional+classification">functional classification</a>; <a href="/?q=ut%3Afunctional+deep+neural+network">functional deep neural network</a>; <a href="/?q=ut%3Afunctional+quadratic+discriminant+analysis">functional quadratic discriminant analysis</a>; <a href="/?q=ut%3AGaussian+process">Gaussian process</a>; <a href="/?q=ut%3Aminimax+excess+misclassification+risk">minimax excess misclassification risk</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 07901853" data-ciurl="/ci/07901853" data-biburl="/bibtex/07901853.bib" data-amsurl="/amsrefs/07901853.bib" data-xmlurl="/xml/07901853.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07901853.pdf" title="Zbl 07901853 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.202022.0057" aria-label="DOI for “Optimal classification for functional data”" title="10.5705/ss.202022.0057">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2103.00569"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Anderson, T. 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Estimation of the mean function of functional data via deep neural networks. Stat 10, e393. · <a href="/07851332" class="nowrap">Zbl 07851332</a></td> </tr><tr> <td>[33]</td> <td class="space">Shuoyang Wang Department of Bioinformatics and Biostatistics, University of Louisville, Louisville, KY 40202, USA. E-mail: shuoyang.wang@louisville.edu Zuofeng Shang Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA. E-mail: zshang@njit.edu Guanqun Cao Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA. E-mail: caoguanq@msu.edu Jun S. Liu Department of Statistics, Harvard University, Cambridge, MA 02138-2901, USA.</td> </tr><tr> <td>[34]</td> <td class="space">E-mail: jliu@stat.harvard.edu (.</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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