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<p>Interval-valued data, a special type of set-valued data, is extensively utilized to describe the imprecision or the vast quantities of data, thereby becoming integral to numerous statistical analyses. In this work, we investigate the problem of detecting multiple change-points on interval-valued time series without prior knowledge of the number and location of the change-points. We introduce a covering rectangle representation of interval-valued data on a two-dimensional coordinate plane and define an LCRI statistic based on it. Subsequently, we develop a novel change-point detection algorithm for interval-valued data by combining the LCRI statistic with segmentation, screening, and peak recognition techniques. The segmentation and screening techniques eliminate regions with no change-points, thus cutting down the computational complexity of this algorithm. The peak recognition techniques improve the robustness and effectiveness of the detection process. Empirical evidence from simulations and real-world datasets demonstrates the superiority of our approach in accuracy and efficiency compared to the existing atheoretical tree algorithm.</p>

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Change-point detection for interval-valued sequences based on the covering rectangle method

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • Li Guan,
  • Jinliang Sun,
  • Ling Liu

摘要

Interval-valued data, a special type of set-valued data, is extensively utilized to describe the imprecision or the vast quantities of data, thereby becoming integral to numerous statistical analyses. In this work, we investigate the problem of detecting multiple change-points on interval-valued time series without prior knowledge of the number and location of the change-points. We introduce a covering rectangle representation of interval-valued data on a two-dimensional coordinate plane and define an LCRI statistic based on it. Subsequently, we develop a novel change-point detection algorithm for interval-valued data by combining the LCRI statistic with segmentation, screening, and peak recognition techniques. The segmentation and screening techniques eliminate regions with no change-points, thus cutting down the computational complexity of this algorithm. The peak recognition techniques improve the robustness and effectiveness of the detection process. Empirical evidence from simulations and real-world datasets demonstrates the superiority of our approach in accuracy and efficiency compared to the existing atheoretical tree algorithm.