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Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process

Author

Listed:
  • Tadas Danielius

    (Institute of Applied Mathematics, Vilnius University, 03225 Vilnius, Lithuania)

  • Alfredas Račkauskas

    (Institute of Applied Mathematics, Vilnius University, 03225 Vilnius, Lithuania)

Abstract

We first define the G -CUSUM process and investigate its theoretical aspects including asymptotic behavior. By choosing different sets G , we propose some tests for multiple change-point detections in a functional sample. We apply the proposed testing procedures to the real-world neurophysiological data and demonstrate how it can identify the existence of the multiple change-points and localize them.

Suggested Citation

  • Tadas Danielius & Alfredas Račkauskas, 2022. "Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process," Mathematics, MDPI, vol. 10(13), pages 1-27, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2294-:d:852753
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    References listed on IDEAS

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    1. István Berkes & Robertas Gabrys & Lajos Horváth & Piotr Kokoszka, 2009. "Detecting changes in the mean of functional observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 927-946, November.
    2. Aston, John A.D. & Kirch, Claudia, 2012. "Detecting and estimating changes in dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 204-220.
    3. Aue, Alexander & Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2009. "Estimation of a change-point in the mean function of functional data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2254-2269, November.
    4. 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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