Document Zbl 07769933

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Sin.</a> <a href="/?q=in%3A505262" title="Articles in this Issue">33, No. 3, 2041-2064 (2023)</a>. </div> <div class="abstract">Summary: Modern statistical analysis often involves large data sets, for which conventional estimation methods are not suitable, owing to limited computational resources. To solve this problem, we propose a novel subsampling-based method with jackknifing. The key idea is to treat the whole sample as if it were the population. Then, we obtain multiple subsamples with greatly reduced sizes using simple random sampling with replacement. We do not recommend sampling methods without replacement, because this would incur a significant data processing cost when the processing occurs on a hard drive. However, such a cost does not exist if the data are processed in memory. Because subsampled data have relatively small sizes, they can be comfortably read into computer memory and processed. Based on subsampled data sets, jackknife-debiased estimators can be obtained for the target parameter. The resulting estimators are statistically consistent, with an extremely small bias. Finally, the jackknife-debiased estimators from different subsamples are averaged to form the final estimator. We show theoretically that the final estimator is consistent and asymptotically normal. Furthermore, its asymptotic statistical efficiency can be as good as that of the whole sample estimator under very mild conditions. The proposed method is easily implemented on most computer systems, and thus is widely applicable.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7769933">Cited in <strong>3</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%3AGPU">GPU</a>; <a href="/?q=ut%3Ajackknife">jackknife</a>; <a href="/?q=ut%3Alarge+dataset">large dataset</a>; <a href="/?q=ut%3Asubsampling">subsampling</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 07769933" data-ciurl="/ci/07769933" data-biburl="/bibtex/07769933.bib" data-amsurl="/amsrefs/07769933.bib" data-xmlurl="/xml/07769933.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07769933.pdf" title="Zbl 07769933 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.202021.0257" aria-label="DOI for “Subsampling and jackknifing: a practically convenient solution for large data analysis with limited computational resources”" title="10.5705/ss.202021.0257">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2304.06231"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">Cameron, A. 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