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Adaptive quantile computation for Brownian bridge in change-point analysis

Author

Listed:
  • Franke, Jürgen
  • Hefter, Mario
  • Herzwurm, André
  • Ritter, Klaus
  • Schwaar, Stefanie

Abstract

As an example for the fast calculation of distributional parameters of Gaussian processes, a new Monte Carlo algorithm for the computation of quantiles of the supremum norm of weighted Brownian bridges is proposed. As it is known, the corresponding distributions arise asymptotically for weighted CUSUM statistics for change-point detection. The new algorithm employs an adaptive (sequential) time discretization for the trajectories of the Brownian bridge. A simulation study shows that the new algorithm by far outperforms the standard approach, which employs a uniform time discretization.

Suggested Citation

  • Franke, Jürgen & Hefter, Mario & Herzwurm, André & Ritter, Klaus & Schwaar, Stefanie, 2022. "Adaptive quantile computation for Brownian bridge in change-point analysis," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321002097
    DOI: 10.1016/j.csda.2021.107375
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    References listed on IDEAS

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    1. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    2. Fumiya Akashi & Holger Dette & Yan Liu, 2018. "Change‐Point Detection in Autoregressive Models with no Moment Assumptions," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(5), pages 763-786, September.
    3. Alexander Aue & Gregory Rice & Ozan Sönmez, 2018. "Detecting and dating structural breaks in functional data without dimension reduction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 509-529, June.
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