Document Zbl 0978.62008

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Stat.</a> <a href="/?q=in%3A65505" title="Articles in this Issue">27, No. 5, 1564-1599 (1999)</a>. </div> <div class="abstract">From the introduction: The metric entropy structure of a density class determines the minimax rate of convergence of density estimators. Here we prove such results using new direct metric entropy bounds on the mutual information that arises by application of Fano’s information inequality in the development of lower bounds characterizing the optimal rate. No special construction is required for each density class. We here study global measures of loss such as integrated squared error, squared Hellinger distance or Kullback-Leibler (K-L) divergence in nonparametric curve estimation problems.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A1496613">Cited in <strong>116</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62B10" title="MSC2020">62B10</a> </td> <td class="space"> Statistical aspects of information-theoretic topics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G07" title="MSC2020">62G07</a> </td> <td class="space"> Density estimation </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62C20" title="MSC2020">62C20</a> </td> <td class="space"> Minimax procedures in statistical decision theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A94A17" title="MSC2020">94A17</a> </td> <td class="space"> Measures of information, entropy </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aminimax+risk">minimax risk</a>; <a href="/?q=ut%3AKullback-Leibler+distance">Kullback-Leibler distance</a>; <a href="/?q=ut%3Ametric+entropy">metric entropy</a></div><div class="keywords"> <h3>Citations:</h3><a href="/0151.24402">Zbl 0151.24402</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 0978.62008" data-ciurl="/ci/01496613" data-biburl="/bibtex/01496613.bib" data-amsurl="/amsrefs/01496613.bib" data-xmlurl="/xml/01496613.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01496613.pdf" title="Zbl 0978.62008 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/1017939142" aria-label="DOI for “Information-theoretic determination of minimax rates of convergence”" title="10.1214/aos/1017939142">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://lib.dr.iastate.edu/stat_las_preprints/103" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ball, K. and Pajor, A. 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