Two multivariate online change detection models

References

• N. Chen, X. Zi, and C. Zou, A distribution-free multivariate control chart, Technometrics 58 (2016), pp. 448–459. doi: 10.1080/00401706.2015.1049750
   Web of Science ®Google Scholar
• R.B. Crosier, Multivariate generalizations of cumulative sum quality-Control schemes, Technometrics 30 (1988), pp. 291–303. doi: 10.1080/00401706.1988.10488402
   Web of Science ®Google Scholar
• O.A. Grigg and D.J. Spiegelhalter, An empirical approximation to the null unbounded steady-state distribution of the cumulative sum statistic, Technometrics 50 (2008), pp. 501–511. doi: 10.1198/004017008000000299
   Web of Science ®Google Scholar
• C. Hartland, N. Baskiotis, S. Gelly, M. Sebag, and O. Teytaud, Change point detection and meta-bandits for online learning in dynamic environments, CAp, Grenoble, France, 2007, pp. 237–250.
   Google Scholar
• H.E.T. Holgersson and P.S. Karlsson, Three estimators of the Mahalanobis distance in high-dimensional data, J. Appl. Stat. 39 (2012), pp. 2713–2720. doi: 10.1080/02664763.2012.725464
   Web of Science ®Google Scholar
• Y. Kawaharal and M. Sugiyama, Fast and accurate detection of changes in data streams, Stat Anal Data Mining 7 (2014), pp. 125–139. doi: 10.1002/sam.11216
   Web of Science ®Google Scholar
• D. Kifer, S. Ben-David, and J. Gehrke, Detecting change in data streams, in Proceedings of the 30th VLDB Conference, Vol. 30, 2004, pp. 180–191,
   Google Scholar
• W. Li, X. Pu, F. Tsung, and D. Xiang, A robust self-starting spatial rank multivariate EWMA chart based on forward variable selection, Comput. Industr. Engin. 103 (2017), pp. 116–130. doi: 10.1016/j.cie.2016.11.024
   Web of Science ®Google Scholar
• W. Li, D. Xiang, F. Tsung, and X. Pu, A diagnostic procedure for high-dimensional data streams via missed discovery rate control, Technometrics 62 (2020), pp. 84–100. doi: 10.1080/00401706.2019.1575284
   Web of Science ®Google Scholar
• Z. Liu and R. Modarres, Lens data depth and median, J. Nonparametric Stat. 23 (2011), pp. 1063–1074. doi: 10.1080/10485252.2011.584621
   Web of Science ®Google Scholar
• R.Y. Liu and K. Singh, A quality index based on data depth and multivariate rank tests, J. Am. Stat. Assoc. 88 (1993), pp. 252–260.
   Web of Science ®Google Scholar
• R. Malladi, G.P. Kalamangalam and B. Aazhang, Online Bayesian change point detection algorithms for segmentation of epileptic activity, In 2013 Asilomar Conference on Signals, Systems and Computers, 2013, pp. 1833–1837.
   Google Scholar
• A. Messaoud, C. Weihs, and F. Hering, A Nonparametric Multivariate Control Chart Based on Data Depth, Technical Report, No. 2004,61, Universität Dortmund, 2004.
   Google Scholar
• D.S. Matteson and N.A. James, A nonparametric approach for multiple change point analysis of multivariate data, J. Am. Stat. Assoc. 109 (2014), pp. 334–345. doi: 10.1080/01621459.2013.849605
   Web of Science ®Google Scholar
• Y. Mei, Efficient scalable schemes for monitoring a large number of data streams, Biometrika 97 (2010), pp. 419–433. doi: 10.1093/biomet/asq010
   Web of Science ®Google Scholar
• J. Mellor and J. Shapiro, Thompson sampling in switching environments with Bayesian online change detection. In 2013 Artificial Intelligence and Statistics, 2013, pp. 442–450,
   Google Scholar
• K. Miyaguchi and K. Yamanishi, Online detection of continuous changes in stochastic processes, Inter. J. Data Sci. Anal. 3 (2017), pp. 213–229. doi: 10.1007/s41060-017-0045-2
   Google Scholar
• R. Modarres and G.P. Patil, Hotspot detection with bivariate data,  Planning and Inference J. Stat. Plan. Inference. 137 (2007), pp. 3643–3654. doi: 10.1016/j.jspi.2007.03.040
   Web of Science ®Google Scholar
• E.S. Page, Continuous inspection schemes, Biometrika 41 (1954), pp. 100–115. doi: 10.1093/biomet/41.1-2.100
   Web of Science ®Google Scholar
• P. Qiu, Introduction to Statistical Process Control, Chapman and Hall/CRC, Florida, 2013.
   Google Scholar
• G.J. Székely and M.L. Rizzo, Energy statistics: A class of statistics based on distances,  Statistical Planning and Inference¡/DIFdel¿J. Stat. Plan. Inference. 143 (2013), pp. 1249–1272. doi: 10.1016/j.jspi.2013.03.018
   Web of Science ®Google Scholar
• P. Yang, G. Dumont, and J.M. Ansermino, An adaptive Cusum test based on a hidden semi-Markov model for change detection in non-invasive mean blood pressure trend. In 2006 International Conference of the IEEE Engineering in Medicine and Biology Society, 2006, pp. 3395–3398,
   Google Scholar
• A. Wald, Sequential Analysis, 1st ed., John Wiley and Sons, New York, 1947.
   Google Scholar
• W. Wei, J. Li, L. Cao, Y. Ou, and J. Chen, Effective detection of sophisticated online banking fraud on extremely imbalanced data, World Wide Web 16 (2013), pp. 449–475. doi: 10.1007/s11280-012-0178-0
   Web of Science ®Google Scholar
• Y. Wu, Streaming techniques for statistical modeling, Doctoral dissertation, Rutgers University-Graduate School-New Brunswick, 2007.
   Google Scholar
• S. Yildirim, S.S. Singh, and A. Doucet, An online expectation–maximization algorithm for changepoint models, J. Comput. Graph. Stat. 22 (2013), pp. 906–926. doi: 10.1080/10618600.2012.674653
   Web of Science ®Google Scholar
• C. Zhang, N. Chen, and J. Wu, Spatial rank-based high-dimensional monitoring through random projection, J. Qual. Technol. 52 (2020), pp. 111–127. doi: 10.1080/00224065.2019.1571336
   Web of Science ®Google Scholar
• C. Zou, W. Jiang, and F. Tsung, A lasso-based diagnostic framework for multivariate statistical process control, Technometrics 53 (2011), pp. 297–309. doi: 10.1198/TECH.2011.10034
   Web of Science ®Google Scholar
• C. Zou and F. Tsung, A multivariate sign EWMA control chart, Technometrics 53 (2011), pp. 84–97. doi: 10.1198/TECH.2010.09095
   Web of Science ®Google Scholar
• C. Zou, Z. Wang, X. Zi, and W. Jiang, An efficient online monitoring method for high-dimensional data streams, Technometrics 57 (2015), pp. 374–387. doi: 10.1080/00401706.2014.940089
   Web of Science ®Google Scholar
• S.T. Bakir, and M.R. Reynolds, A nonparametric procedure for process control based on within-group ranking, Technometrics 21 (1979), pp. 175–183. doi: 10.1080/00401706.1979.10489747
   Web of Science ®Google Scholar
• S. Chakraborti, and M.A. Van de Wiel, A Nonparametric Control Chart Based on the Mann-Whitney Statistic, Institute of Mathematical Statistics, Ohio, 2008.
   Google Scholar
• J. Li, Efficient global monitoring statistics for high?dimensional data, Quality and Reliability Engineering International 36 (2020), pp. 18–32. doi: 10.1002/qre.2557
   Web of Science ®Google Scholar