Multiple change point detection for high-dimensional data

• Wenbiao Zhao ^[1] ; Lixing Zhu ^[3] ; Falong Tan ^[2]
  1. [1] Beijing Institute of Technology

     Beijing Institute of Technology

     China

     
  2. [2] Hunan University

     Hunan University

     China

     
  3. [3] Beijing Normal University at Zhuhai

  Mostrar afiliaciones +
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 33, Nº. 3, 2024, págs. 809-846
• Idioma: inglés
• DOI: 10.1007/s11749-024-00926-w
• Texto completo no disponible (Saber más ...)
• Resumen

  • This research investigates the detection of multiple change points in high-dimensional data without particular sparse or dense structure, where the dimension can be of exponential order in relation to the sample size. The estimation approach proposed employs a signal statistic based on a sequence of signal screening-based local U-statistics. This technique avoids costly computations that exhaustive search algorithms require and mitigates false positives, which hypothesis testing-based methods need to control. Consistency of estimation can be achieved for both the locations and number of change points, even when the number of change points diverges at a certain rate as the sample size increases. Additionally, the visualization nature of the proposed approach makes plotting the signal statistic a useful tool to identify locations of change points, which distinguishes it from existing methods in the literature. Numerical studies are performed to evaluate the effectiveness of the proposed technique in finite sample scenarios, and a real data analysis is presented to illustrate its application.