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We develop a simple CUSUM-based methodology that provably control the probability of false alarms or the average run length while minimizing, in a minimax sense, the detection delay. We allow for all the model parameters to vary in order to capture a broad range of levels of statistical hardness for the problem at hand. We further show how our methodology is applicable to the case in which multiple change points are to be estimated sequentially.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7785272">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%3A62Lxx" title="MSC2020">62Lxx</a> </td> <td class="space"> Sequential statistical methods </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aonline+change+point+detection">online change point detection</a>; <a href="/?q=ut%3Acumulative+sum+statistics">cumulative sum statistics</a></div> <div class="software"> <h3>Software:</h3><a href="/software/47886">gStream</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07785272" data-ciurl="/ci/07785272" data-biburl="/bibtex/07785272.bib" data-amsurl="/amsrefs/07785272.bib" data-xmlurl="/xml/07785272.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07785272.pdf" title="Zbl 07785272 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/10.1080/07474946.2023.2276170" aria-label="DOI for “A note on online change point detection”" title="10.1080/07474946.2023.2276170">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2006.03283"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aue, Alexander, and Horváth, Lajos. 2004. “Delay Time in Sequential Detection of Change.” Statistics & Probability Letters67 (3): 221-231. · <a href="/1059.62085" class="nowrap">Zbl 1059.62085</a></td> </tr><tr> <td>[2]</td> <td class="space">Aue, Alexander, Horváth, Lajos, and Reimherr, Matthew L.. 2009. “Delay Times of Sequential Procedures for Multiple Time Series Regression Models.” Journal of Econometrics149 (2): 174-190. · <a href="/1429.62380" class="nowrap">Zbl 1429.62380</a></td> </tr><tr> <td>[3]</td> <td class="space">Chen, Guangliang, Atev, Stefan, and Lerman, Gilad. 2009. “Kernel Spectral Curvature Clustering (KSCC).” In 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops, , Kyoto, Japan, 27 September-4 October 2009, 765-772. 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In some cases that data have been complemented/enhanced by data from zbMATH Open. 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