Document Zbl 1360.62184

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Stat.</a> <a href="/?q=in%3A256067" title="Articles in this Issue">37, No. 6B, 3743-3778 (2009)</a>. </div> <div class="abstract">Summary: In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their structural dimensions are no larger than that of the central subspace [<span class="zbmathjax-textit">R. D. Cook</span>, Regression graphics. Ideas for studying regressions through graphics. New York, NY: Wiley (1998; <a href="/0903.62001">Zbl 0903.62001</a>)]. Furthermore, we employ CP-sliced inverse regression, CP-sliced average variance estimation and CP-directional regression to estimate the generalized contour subspace, and we subsequently obtain their theoretical properties. Monte Carlo studies demonstrate that the three CP-based dimension reduction methods outperform their corresponding non-CP approaches when the predictors have heavy-tailed elliptical distributions. An empirical example is also presented to illustrate the usefulness of the CP method.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5644255">Cited in <strong>30</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G08" title="MSC2020">62G08</a> </td> <td class="space"> Nonparametric regression and quantile regression </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G35" title="MSC2020">62G35</a> </td> <td class="space"> Nonparametric robustness </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G20" title="MSC2020">62G20</a> </td> <td class="space"> Asymptotic properties of nonparametric inference </td> </tr><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%3A62J99" title="MSC2020">62J99</a> </td> <td class="space"> Linear inference, regression </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Acentral+subspace">central subspace</a>; <a href="/?q=ut%3Acentral+contour+subspace">central contour subspace</a>; <a href="/?q=ut%3Acontour+projection">contour projection</a>; <a href="/?q=ut%3Adirectional+regression">directional regression</a>; <a href="/?q=ut%3Ageneralized+contour+subspace">generalized contour subspace</a>; <a href="/?q=ut%3Akernel+contour+subspace">kernel contour subspace</a>; <a href="/?q=ut%3A%5C%28%5Csqrt%7Bn%7D%5C%29-consistency">$\sqrt{n}$-consistency</a>; <a href="/?q=ut%3Asliced+average+variance+estimation">sliced average variance estimation</a>; <a href="/?q=ut%3Asliced+inverse+regression">sliced inverse regression</a>; <a href="/?q=ut%3Asufficient+contour+subspace">sufficient contour subspace</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0903.62001">Zbl 0903.62001</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 1360.62184" data-ciurl="/ci/05644255" data-biburl="/bibtex/05644255.bib" data-amsurl="/amsrefs/05644255.bib" data-xmlurl="/xml/05644255.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05644255.pdf" title="Zbl 1360.62184 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/10.1214/08-AOS679" aria-label="DOI for “Contour projected dimension reduction”" title="10.1214/08-AOS679">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/0911.3481"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">Chiaromonte, F., Cook, R. 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