Document Zbl 07785272

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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>  <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 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. IEEE.</td> </tr><tr> <td>[4]</td> <td class="space">Chen, Hao.2019. “Sequential Change-Point Detection Based on Nearest Neighbors.” The Annals of Statistics47 (3): 1381-1407. · <a href="/1419.62201" class="nowrap">Zbl 1419.62201</a></td> </tr><tr> <td>[5]</td> <td class="space">Chen, Hao, and Chu, Lynna. 2019. “gStream: Graph-Based Sequential Change-Point Detection for Streaming Data.” R package version 0.2.0. https://cran.r-project.org/web/packages/gStream/index.html · <a href="/1417.62114" class="nowrap">Zbl 1417.62114</a></td> </tr><tr> <td>[6]</td> <td class="space">Chen, Yudong, Wang, Tengyao, and Samworth, Richard J.. 2020. “High-Dimensional, Multiscale Online Changepoint Detection.” arXiv preprint arXiv: 2003.03668. · <a href="/07593410" class="nowrap">Zbl 07593410</a></td> </tr><tr> <td>[7]</td> <td class="space">Chu, Chia-Shang James, Stinchcombe, Maxwell, and White, Halbert. 1996. “Monitoring Structural Change.” Econometrica64 (5): 1045. · <a href="/0856.90027" class="nowrap">Zbl 0856.90027</a></td> </tr><tr> <td>[8]</td> <td class="space">Desobry, Frédéric, Davy, Manuel, and Doncarli, Christian. 2005. “An Online Kernel Change Detection Algorithm.” IEEE Transactions on Signal Processing53 (8): 2961-2974. · <a href="/1370.94317" class="nowrap">Zbl 1370.94317</a></td> </tr><tr> <td>[9]</td> <td class="space">Dette, Holger, and Gösmann, Josua. 2020. “A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters.” Journal of the American Statistical Association115 (531): 1361-1377. · <a href="/1441.62212" class="nowrap">Zbl 1441.62212</a></td> </tr><tr> <td>[10]</td> <td class="space">Fearnhead, Paul, and Liu, Zhen. 2007. “On-Line Inference for Multiple Changepoint Problems.” Journal of the Royal Statistical Society Series B: Statistical Methodology69 (4): 589-605. · <a href="/07555366" class="nowrap">Zbl 07555366</a></td> </tr><tr> <td>[11]</td> <td class="space">Gösmann, Josua, Kley, Tobias, and Dette, Holger. 2019. “A New Approach for Open-End Sequential Change Point Monitoring.” arXiv preprint arXiv: 1906.03225. · <a href="/1468.62338" class="nowrap">Zbl 1468.62338</a></td> </tr><tr> <td>[12]</td> <td class="space">He, Xi, Xie, Yao, Wu, Sin-Mei, and Lin, Fan-Chi. 2018. “Sequential Graph Scanning Statistic for Change-Point Detection.” In 2018 52nd Asilomar Conference on Signals, Systems, and Computers, , Pacific Grove, CA, USA, 1317-1321. IEEE.</td> </tr><tr> <td>[13]</td> <td class="space">Hlávka, Zdenek, Husková, Marie, Kirch, Claudia, and Meintanis, Simos G.. 2016. “Bootstrap Procedures for Online Monitoring of Changes in Autoregressive Models.” Communications in Statistics—Simulation and Computation45 (7): 2471-2490. · <a href="/1351.62167" class="nowrap">Zbl 1351.62167</a></td> </tr><tr> <td>[14]</td> <td class="space">Howard, Steven R., Ramdas, Aaditya, McAuliffe, Jon, and Sekhon, Jasjeet. 2018. “Uniform, Nonparametric, Non-Asymptotic Confidence Sequences.” arXiv preprint arXiv: 1810.08240. · <a href="/1476.62170" class="nowrap">Zbl 1476.62170</a></td> </tr><tr> <td>[15]</td> <td class="space">Husková, Marie, and Kirch, Claudia. 2012. “Bootstrapping Sequential Change-Point Tests for Linear Regression.” Metrika75 (5): 673-708. · <a href="/1362.62161" class="nowrap">Zbl 1362.62161</a></td> </tr><tr> <td>[16]</td> <td class="space">Husková, Marie, Kirch, Claudia, and Meintanis, Simos G.. 2010. “Fourier Methods for Sequential Change Point Analysis in Autoregressive Models.” In Proceedings of COMPSTAT’2010, , 501-508. Limassol, Cyprus: Springer. · <a href="/1436.62426" class="nowrap">Zbl 1436.62426</a></td> </tr><tr> <td>[17]</td> <td class="space">Keshavarz, Hossein, Michailidis, George, and Atchade, Yves. 2018. “Sequential Change-Point Detection in High-Dimensional Gaussian Graphical Models.” arXiv preprint arXiv: 1806.07870. · <a href="/1499.62194" class="nowrap">Zbl 1499.62194</a></td> </tr><tr> <td>[18]</td> <td class="space">Kirch, Claudia.2008. “Bootstrapping Sequential Change-Point Tests.” Sequential Analysis27 (3): 330-349. · <a href="/1145.62060" class="nowrap">Zbl 1145.62060</a></td> </tr><tr> <td>[19]</td> <td class="space">Kirch, Claudia, and Weber, Silke. 2018. “Modified Sequential Change Point Procedures Based on Estimating Functions.” Electronic Journal of Statistics12 (1): 1579-1613. · <a href="/1392.62241" class="nowrap">Zbl 1392.62241</a></td> </tr><tr> <td>[20]</td> <td class="space">Kurt, Mehmet Necip, Yilmaz, Yasin, and Wang, Xiaodong. 2018. “Real-Time Nonparametric Anomaly Detection in High-Dimensional Settings.” arXiv preprint arXiv: 1809.05250.</td> </tr><tr> <td>[21]</td> <td class="space">Lai, Tze Leung.1981. “Asymptotic Optimality of Invariant Sequential Probability Ratio Tests.” The Annals of Statistics9 (2): 318-333. · <a href="/0459.62069" class="nowrap">Zbl 0459.62069</a></td> </tr><tr> <td>[22]</td> <td class="space">Lai, Tze Leung.1995. “Sequential Changepoint Detection in Quality Control and Dynamical Systems.” Journal of the Royal Statistical Society: Series B (Methodological)57 (4): 613-644. · <a href="/0832.62072" class="nowrap">Zbl 0832.62072</a></td> </tr><tr> <td>[23]</td> <td class="space">Lai, Tze Leung.1998. “Information Bounds and Quick Detection of Parameter Changes in Stochastic Systems.” IEEE Transactions on Information Theory44 (7): 2917-2929. · <a href="/0955.62084" class="nowrap">Zbl 0955.62084</a></td> </tr><tr> <td>[24]</td> <td class="space">Lai, Tze Leung.2001. “Sequential Analysis: some Classical Problems and New Challenges.” Statistica Sinica11 (2): 303-351. · <a href="/1037.62081" class="nowrap">Zbl 1037.62081</a></td> </tr><tr> <td>[25]</td> <td class="space">Lorden, Gary.1971. “Procedures for Reacting to a Change in Distribution.” The Annals of Mathematical Statistics42 (6): 1897-1908. · <a href="/0255.62067" class="nowrap">Zbl 0255.62067</a></td> </tr><tr> <td>[26]</td> <td class="space">Maillard, Odalric-Ambrym.2019. “Sequential Change-Point Detection: Laplace Concentration of Scan Statistics and Non-Asymptotic Delay Bounds.” In Algorithmic Learning Theory, 610-632. PMLR. · <a href="/07977709" class="nowrap">Zbl 07977709</a></td> </tr><tr> <td>[27]</td> <td class="space">Mei, Yajun.2010. “Efficient Scalable Schemes for Monitoring a Large Number of Data Streams.” Biometrika97 (2): 419-433. · <a href="/1406.62088" class="nowrap">Zbl 1406.62088</a></td> </tr><tr> <td>[28]</td> <td class="space">Moustakides, George V.1986. “Optimal Stopping Times for Detecting Changes in Distributions.” The Annals of Statistics14 (4): 1379-1387. · <a href="/0612.62116" class="nowrap">Zbl 0612.62116</a></td> </tr><tr> <td>[29]</td> <td class="space">Namoano, Bernadin, Starr, Andrew, Emmanouilidis, Christos, and Cristobal, Ruiz Carcel. 2019. “Online Change Detection Techniques in Time Series: An Overview.” In 2019 IEEE International Conference on Prognostics and Health Management (ICPHM), , San Francisco, CA, USA, 1-10. IEEE.</td> </tr><tr> <td>[30]</td> <td class="space">Page, Ewan S.1954. “Continuous Inspection Schemes.” Biometrika41 (1-2): 100-115. · <a href="/0056.38002" class="nowrap">Zbl 0056.38002</a></td> </tr><tr> <td>[31]</td> <td class="space">Ritov, Ya’acov.1990. “Decision Theoretic Optimality of the CUSUM Procedure.” The Annals of Statistics18 (3): 1464-1469. · <a href="/0712.62073" class="nowrap">Zbl 0712.62073</a></td> </tr><tr> <td>[32]</td> <td class="space">Siegmund, David.2013. Sequential Analysis: tests and Confidence Intervals. New York: Springer Science & Business Media. · <a href="/0573.62071" class="nowrap">Zbl 0573.62071</a></td> </tr><tr> <td>[33]</td> <td class="space">Tartakovsky, Alexander, Nikiforov, Igor, and Basseville, Michele. 2014. Sequential Analysis: Hypothesis Testing and Changepoint Detection. Boca Raton, FL: Chapman and Hall/CRC. · <a href="/1341.62026" class="nowrap">Zbl 1341.62026</a></td> </tr><tr> <td>[34]</td> <td class="space">Wainwright, Martin J.2019. High-Dimensional Statistics: A Non-Asymptotic Viewpoint. Vol. 48. Cambridge, UK: Cambridge University Press. · <a href="/1457.62011" class="nowrap">Zbl 1457.62011</a></td> </tr><tr> <td>[35]</td> <td class="space">Wald, A.1945. “Sequential Tests of Statistical Hypotheses.” The Annals of Mathematical Statistics16 (2): 117-186. · <a href="/0060.30207" class="nowrap">Zbl 0060.30207</a></td> </tr><tr> <td>[36]</td> <td class="space">Wang, Daren, Yu, Yi, and Rinaldo, Alessandro. 2020. “Univariate Mean Change Point Detection: Penalization, Cusum and Optimality.” Electronic Journal of Statistics14 (1): 1917-1961. · <a href="/1442.62097" class="nowrap">Zbl 1442.62097</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. 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