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Bootstrap confidence intervals for multiple change points based on moving sum procedures

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  • Cho, Haeran
  • Kirch, Claudia

Abstract

The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum statistics is derived, where the limit distributions differ depending on whether the corresponding size of changes is local, i.e. tends to zero as the sample size increases, or fixed. A bootstrap procedure for confidence interval generation is proposed which adapts to the unknown magnitude of changes and guarantees asymptotic validity both for local and fixed changes. Simulation studies show good performance of the proposed bootstrap procedure, and some discussions about how it can be extended to serially dependent errors are provided.

Suggested Citation

  • Cho, Haeran & Kirch, Claudia, 2022. "Bootstrap confidence intervals for multiple change points based on moving sum procedures," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:csdana:v:175:y:2022:i:c:s0167947322001323
    DOI: 10.1016/j.csda.2022.107552
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    References listed on IDEAS

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    1. Klaus Frick & Axel Munk & Hannes Sieling, 2014. "Multiscale change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 495-580, June.
    2. Chun Yip Yau & Zifeng Zhao, 2016. "Inference for multiple change points in time series via likelihood ratio scan statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 895-916, September.
    3. 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.
    4. Antoch, Jaromír & Husková, Marie, 2001. "Permutation tests in change point analysis," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 37-46, May.
    5. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    6. Marie Hušková & Claudia Kirch, 2010. "A note on studentized confidence intervals for the change-point," Computational Statistics, Springer, vol. 25(2), pages 269-289, June.
    7. Sangwon Hyun & Kevin Z. Lin & Max G'Sell & Ryan J. Tibshirani, 2021. "Post‐selection inference for changepoint detection algorithms with application to copy number variation data," Biometrics, The International Biometric Society, vol. 77(3), pages 1037-1049, September.
    8. Christopher F. H. Nam & John A. D. Aston & Adam M. Johansen, 2012. "Quantifying the uncertainty in change points," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(5), pages 807-823, September.
    9. Inder Tecuapetla-Gómez & Axel Munk, 2017. "Autocovariance Estimation in Regression with a Discontinuous Signal and m-Dependent Errors: A Difference-Based Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 346-368, June.
    10. Dietmar Ferger, 2004. "A continuous mapping theorem for the argmax‐functional in the non‐unique case," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 83-96, February.
    11. Marie Hušková & Claudia Kirch, 2008. "Bootstrapping confidence intervals for the change‐point of time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 947-972, November.
    12. Ery Arias-Castro & Rui M. Castro & Ervin Tánczos & Meng Wang, 2018. "Distribution-Free Detection of Structured Anomalies: Permutation and Rank-Based Scans," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 789-801, April.
    13. 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.
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