R package HSMUCE: Implementation of H-SMUCE. We propose, a heterogeneous simultaneous multiscale change point estimator called ‘H‐SMUCE’ for the detection of multiple change points of the signal in a heterogeneous Gaussian regression model. A piecewise constant function is estimated by minimizing the number of change points over the acceptance region of a multiscale test which locally adapts to changes in the variance. The multiscale test is a combination of local likelihood ratio tests which are properly calibrated by scale‐dependent critical values to keep a global nominal level α, even for finite samples. We show that H‐SMUCE controls the error of overestimation and underestimation of the number of change points. For this, new deviation bounds for F‐type statistics are derived. Moreover, we obtain confidence sets for the whole signal. All results are non‐asymptotic and uniform over a large class of heterogeneous change point models. H‐SMUCE is fast to compute, achieves the optimal detection rate and estimates the number of change points at almost optimal accuracy for vanishing signals, while still being robust. We compare H‐SMUCE with several state of the art methods in simulations and analyse current recordings of a transmembrane protein in the bacterial outer membrane with pronounced heterogeneity for its states. An R‐package is available on line.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Datta, Pratyay; Sen, Bodhisattva: Optimal inference with a multidimensional multiscale statistic (2021)
  2. Kang, Sang Gil; Lee, Woo Dong; Kim, Yongku: Bayesian multiple change-points detection in a normal model with heterogeneous variances (2021)
  3. Madrid Padilla, Oscar Hernan; Yu, Yi; Wang, Daren; Rinaldo, Alessandro: Optimal nonparametric change point analysis (2021)
  4. Du, Chao; Kou, S. C.: Statistical methodology in single-molecule experiments (2020)
  5. Enikeeva, Farida; Munk, Axel; Pohlmann, Markus; Werner, Frank: Bump detection in the presence of dependency: does it ease or does it load? (2020)
  6. Baranowski, Rafal; Chen, Yining; Fryzlewicz, Piotr: Narrowest-over-threshold detection of multiple change points and change-point-like features (2019)
  7. Li, Housen; Guo, Qinghai; Munk, Axel: Multiscale change-point segmentation: beyond step functions (2019)
  8. Li, Yingbo; Lund, Robert; Hewaarachchi, Anuradha: Multiple changepoint detection with partial information on changepoint times (2019)
  9. Messer, Michael; Albert, Stefan; Schneider, Gaby: The multiple filter test for change point detection in time series (2018)
  10. Yi, Taihe; Wang, Zhengming; Yi, Dongyun: Bayesian sieve methods: approximation rates and adaptive posterior contraction rates (2018)
  11. Pein, Florian: Heterogeneous multiscale change-point inference and its application to ion channel recordings (2017)
  12. Pein, Florian; Sieling, Hannes; Munk, Axel: Heterogeneous change point inference (2017)
  13. Yi, Taihe; Wang, Zhengming: Bayesian sieve method for piece-wise smooth regression (2017)