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High dimensional change point inference: Recent developments and extensions

Author

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  • Liu, Bin
  • Zhang, Xinsheng
  • Liu, Yufeng

Abstract

Change point analysis aims to detect structural changes in a data sequence. It has always been an active research area since it was introduced in the 1950s. In modern statistical applications, however, high-throughput data with increasing dimensions are ubiquitous in fields ranging from economics, finance to genetics and engineering. For those problems, the earlier works are typically no longer applicable. As a result, the problem of testing a change point for high dimensional data sequences has been an important yet challenging task. In this paper, we first focus on models for at most one change point, and review recent state-of-art techniques for change point testing of high dimensional mean vectors and compare their theoretical properties. Based on that, we provide a survey of some extensions to general high dimensional parameters beyond mean vectors as well as strategies for testing multiple change points in high dimensions. Finally, we discuss some open problems for possible future research directions.

Suggested Citation

  • Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:jmvana:v:188:y:2022:i:c:s0047259x21001111
    DOI: 10.1016/j.jmva.2021.104833
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    References listed on IDEAS

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    1. Nancy R. Zhang & David O. Siegmund & Hanlee Ji & Jun Z. Li, 2010. "Detecting simultaneous changepoints in multiple sequences," Biometrika, Biometrika Trust, vol. 97(3), pages 631-645.
    2. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.
    3. Jirak, Moritz, 2012. "Change-point analysis in increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 136-159.
    4. Michael Messer & Stefan Albert & Gaby Schneider, 2018. "The multiple filter test for change point detection in time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 589-607, August.
    5. Mengjia Yu & Xiaohui Chen, 2021. "Finite sample change point inference and identification for high‐dimensional mean vectors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 247-270, April.
    6. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    7. Haeran Cho & Piotr Fryzlewicz, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 475-507, March.
    8. Ting Zhang & Liliya Lavitas, 2018. "Unsupervised Self-Normalized Change-Point Testing for Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 637-648, April.
    9. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    10. Rafal Baranowski & Yining Chen & Piotr Fryzlewicz, 2019. "Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 649-672, July.
    11. Tengyao Wang & Richard J. Samworth, 2018. "High dimensional change point estimation via sparse projection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 57-83, January.
    12. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2016. "The lasso for high dimensional regression with a possible change point," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 193-210, January.
    13. Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    14. Monika Bours & Ansgar Steland, 2021. "Large‐sample approximations and change testing for high‐dimensional covariance matrices of multivariate linear time series and factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 610-654, June.
    15. Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    16. Lajos Horváth & Gregory Rice, 2014. "Rejoinder on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 287-290, June.
    17. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
    18. Shao, Xiaofeng & Zhang, Xianyang, 2010. "Testing for Change Points in Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1228-1240.
    19. Bin Liu & Cheng Zhou & Xinsheng Zhang & Yufeng Liu, 2020. "A unified data‐adaptive framework for high dimensional change point detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 933-963, September.
    20. Guo, Xiao & Zhang, Hai & Wang, Yao & Wu, Jiang-Lun, 2015. "Model selection and estimation in high dimensional regression models with group SCAD," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 86-92.
    21. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    22. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    23. Marie Hušková & Simos Meintanis, 2006. "Change Point Analysis based on Empirical Characteristic Functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 145-168, April.
    24. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
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    Cited by:

    1. Jiang, Feiyu & Wang, Runmin & Shao, Xiaofeng, 2023. "Robust inference for change points in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

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