Window-sliding based NSP algorithm for multiple change-points estimation

Xiaoyuan Zhang; Zhanshou Chen; Xiaoyuan Zhang; Zhanshou Chen

doi:10.3934/math.20251311

AIMS Mathematics

2025, Volume 10, Issue 12: 29853-29872. doi: 10.3934/math.20251311

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Window-sliding based NSP algorithm for multiple change-points estimation

Xiaoyuan Zhang ¹,
Zhanshou Chen ^{1,2
,
,}

1.
School of Mathematics and Statistics, Qinghai Normal University, Xining, China
2.
The State Key Laboratory of Tibetan Intelligence, Qinghai Normal University, Xining 810008, China

Received: 28 September 2025 Revised: 06 December 2025 Accepted: 12 December 2025 Published: 18 December 2025
MSC : 62F03, 62L10

A window-sliding based narrowest significance pursuit (WNSP) algorithm is proposed for multiple change-points estimation. The algorithm adopts a "post-inference selection" approach: first, it automatically identifies the narrowest significant intervals containing at least one change point using the narrow significance tracking (NSP) method at a global significance level $ \alpha $; then, within each interval, it employs adaptive bandwidth and single-peak detection techniques to achieve precise estimation of change-point locations. Theoretical analysis confirms the method's consistency and finite-sample reliability under general noise conditions. Numerical simulations and real-world data analysis demonstrate the WNSP algorithm's effectiveness and robustness across diverse noise distributions and signal structures.
- change-points estimation,
- window-sliding,
- narrowest significance pursuit,
- confidence intervals,
- local statistic
Citation: Xiaoyuan Zhang, Zhanshou Chen. Window-sliding based NSP algorithm for multiple change-points estimation[J]. AIMS Mathematics, 2025, 10(12): 29853-29872. doi: 10.3934/math.20251311

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Abstract

A window-sliding based narrowest significance pursuit (WNSP) algorithm is proposed for multiple change-points estimation. The algorithm adopts a "post-inference selection" approach: first, it automatically identifies the narrowest significant intervals containing at least one change point using the narrow significance tracking (NSP) method at a global significance level $ \alpha $; then, within each interval, it employs adaptive bandwidth and single-peak detection techniques to achieve precise estimation of change-point locations. Theoretical analysis confirms the method's consistency and finite-sample reliability under general noise conditions. Numerical simulations and real-world data analysis demonstrate the WNSP algorithm's effectiveness and robustness across diverse noise distributions and signal structures.

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