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Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features

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  • Rafal Baranowski
  • Yining Chen
  • Piotr Fryzlewicz

Abstract

We propose a new, generic and flexible methodology for non‐parametric function estimation, in which we first estimate the number and locations of any features that may be present in the function and then estimate the function parametrically between each pair of neighbouring detected features. Examples of features handled by our methodology include change points in the piecewise constant signal model, kinks in the piecewise linear signal model and other similar irregularities, which we also refer to as generalized change points. Our methodology works with only minor modifications across a range of generalized change point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalized change point detection device, termed narrowest‐over‐threshold (NOT) detection. The key ingredient of the NOT method is its focus on the smallest local sections of the data on which the existence of a feature is suspected. For selected scenarios, we show the consistency and near optimality of the NOT algorithm in detecting the number and locations of generalized change points. The NOT estimators are easy to implement and rapid to compute. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. Our methodology is implemented in the R package not.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:81:y:2019:i:3:p:649-672
    DOI: 10.1111/rssb.12322
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    Cited by:

    1. Cai, Hanqing & Wang, Tengyao, 2023. "Estimation of high-dimensional change-points under a group sparsity structure," LSE Research Online Documents on Economics 118366, London School of Economics and Political Science, LSE Library.
    2. Haeran Cho & Claudia Kirch, 2022. "Two-stage data segmentation permitting multiscale change points, heavy tails and dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 653-684, August.
    3. Chen, Yudong & Wang, Tengyao & Samworth, Richard J., 2022. "High-dimensional, multiscale online changepoint detection," LSE Research Online Documents on Economics 113665, London School of Economics and Political Science, LSE Library.
    4. Andreas Anastasiou & Piotr Fryzlewicz, 2022. "Detecting multiple generalized change-points by isolating single ones," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 141-174, February.
    5. McGonigle, Euan T. & Cho, Haeran, 2023. "Robust multiscale estimation of time-average variance for time series segmentation," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    6. Yudong Chen & Tengyao Wang & Richard J. Samworth, 2022. "High‐dimensional, multiscale online changepoint detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 234-266, February.
    7. Jiang, Feiyu & Zhao, Zifeng & Shao, Xiaofeng, 2023. "Time series analysis of COVID-19 infection curve: A change-point perspective," Journal of Econometrics, Elsevier, vol. 232(1), pages 1-17.
    8. Cui, Junfeng & Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2023. "Change-point testing for parallel data sets with FDR control," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    9. Geon Lee & Se-eun Yoon & Kijung Shin, 2022. "Simple epidemic models with segmentation can be better than complex ones," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-18, January.
    10. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Julia Nasiadka & Weronika Nitka & Rafa{l} Weron, 2022. "Calibration window selection based on change-point detection for forecasting electricity prices," Papers 2204.00872, arXiv.org.
    12. Holger Dette & Theresa Eckle & Mathias Vetter, 2020. "Multiscale change point detection for dependent data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1243-1274, December.
    13. Canhong Wen & Xueqin Wang & Aijun Zhang, 2023. "ℓ 0 Trend Filtering," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1491-1510, November.
    14. Chen, Yining, 2020. "Jump or kink: note on super-efficiency in segmented linear regression break-point estimation," LSE Research Online Documents on Economics 103488, London School of Economics and Political Science, LSE Library.

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