Document Zbl 1012.62042

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(With discussion).</strong> <i>(English)</i> <a class="label nowrap" href="/1012.62042">Zbl 1012.62042</a> </h2> <div class="source"> <a href="/serials/319" title="Journal Profile">Ann. Stat.</a> <a href="/?q=in%3A89977" title="Articles in this Issue">30, No. 2, 325-396 (2002)</a>. </div> <div class="abstract">Summary: In the context of minimax theory, we propose a new kind of risk, normalized by a random variable, measurable with respect to the data. We present a notion of optimality and a method to construct optimal procedures accordingly. We apply this general setup to the problem of selecting significant variables in Gaussian white noise. In particular, we show that our method essentially improves the accuracy of estimation, in the sense of giving explicit improved confidence sets in $L_2$-norm. Links to adaptive estimation are discussed.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1829086">Cited in <strong>49</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%3A62M10" title="MSC2020">62M10</a> </td> <td class="space"> Time series, auto-correlation, regression, etc. in statistics (GARCH) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G15" title="MSC2020">62G15</a> </td> <td class="space"> Nonparametric tolerance and confidence regions </td> </tr></table> </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 1012.62042" data-ciurl="/ci/01829086" data-biburl="/bibtex/01829086.bib" data-amsurl="/amsrefs/01829086.bib" data-xmlurl="/xml/01829086.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01829086.pdf" title="Zbl 1012.62042 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/aos/1021379858" aria-label="DOI for “Random rates in anisotropic regression. (With discussion)”" title="10.1214/aos/1021379858">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">AKAIKE, H. (1974). A new look at the statistical model identification. IEEE Trans. Automat. Control 19 716-723. · <a href="/0314.62039" class="nowrap">Zbl 0314.62039</a> · <a href="https://doi.org/10.1109/TAC.1974.1100705" class="nowrap">doi:10.1109/TAC.1974.1100705</a></td> </tr><tr> <td>[2]</td> <td class="space">BARRON, A., BIRGÉ, L. and MASSART, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 301-413. · <a href="/0946.62036" class="nowrap">Zbl 0946.62036</a> · <a href="https://doi.org/10.1007/s004400050210" class="nowrap">doi:10.1007/s004400050210</a></td> </tr><tr> <td>[3]</td> <td class="space">BREIMAN, L. and FREEDMAN, D. (1983). How many variables should be entered in a regression model? J. Amer. Statist. Assoc. 78 131-136. 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