FDR-control in multiscale change-point segmentation. Fast multiple change-point segmentation methods, which additionally provide faithful statistical statements on the number, locations and sizes of the segments, have recently received great attention. In this paper, we propose a multiscale segmentation method, FDRSeg, which controls the false discovery rate (FDR) in the sense that the number of false jumps is bounded linearly by the number of true jumps. In this way, it adapts the detection power to the number of true jumps. We prove a non-asymptotic upper bound for its FDR in a Gaussian setting, which allows to calibrate the only parameter of FDRSeg properly. Moreover, we show that FDRSeg estimates change-point locations, as well as the signal, in a uniform sense at optimal minimax convergence rates up to a log-factor. The latter is w.r.t. $L^{p}$-risk, $pgeq 1$, over classes of step functions with bounded jump sizes and either bounded, or even increasing, number of change-points. FDRSeg can be efficiently computed by an accelerated dynamic program; its computational complexity is shown to be linear in the number of observations when there are many change-points. The performance of the proposed method is examined by comparisons with some state of the art methods on both simulated and real datasets. An R-package is available online.

References in zbMATH (referenced in 14 articles )

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  1. Alexander Meier, Claudia Kirch, Haeran Cho: mosum: A Package for Moving Sums in Change-Point Analysis (2021) not zbMATH
  2. Peiliang Bai, Yue Bai, Abolfazl Safikhani, George Michailidis: Multiple Change Point Detection in Structured VAR Models: the VARDetect R Package (2021) arXiv
  3. Cheng, Dan; He, Zhibing; Schwartzman, Armin: Multiple testing of local extrema for detection of change points (2020)
  4. Gao, Chao; Han, Fang; Zhang, Cun-Hui: On estimation of isotonic piecewise constant signals (2020)
  5. Hahn, Georg; Fearnhead, Paul; Eckley, Idris A.: BayesProject: fast computation of a projection direction for multivariate changepoint detection (2020)
  6. K├Ânig, Claudia; Munk, Axel; Werner, Frank: Multidimensional multiscale scanning in exponential families: limit theory and statistical consequences (2020)
  7. Ma, Lijing; Grant, Andrew J.; Sofronov, Georgy: Multiple change point detection and validation in autoregressive time series data (2020)
  8. Andreas Anastasiou, Piotr Fryzlewicz: Detecting multiple generalized change-points by isolating single ones (2019) arXiv
  9. Li, Housen; Guo, Qinghai; Munk, Axel: Multiscale change-point segmentation: beyond step functions (2019)
  10. Chengcheng Huang, Housen Li, Lizhi Cheng, Wei Peng: A linear time algorithm for multiscale quantile simulation (2018) arXiv
  11. Fryzlewicz, Piotr: Tail-greedy bottom-up data decompositions and fast multiple change-point detection (2018)
  12. Pein, Florian: Heterogeneous multiscale change-point inference and its application to ion channel recordings (2017)
  13. Yi, Taihe; Wang, Zhengming: Bayesian sieve method for piece-wise smooth regression (2017)
  14. Li, Housen; Munk, Axel; Sieling, Hannes: FDR-control in multiscale change-point segmentation (2016)