Break Point Detection for Functional Covariance

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

2 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)477-512
Journal / PublicationScandinavian Journal of Statistics
Volume50
Issue number2
Online published18 Apr 2022
Publication statusPublished - Jun 2023
Externally publishedYes

Abstract

Many neuroscience experiments record sequential trajectories where each trajectory consists of oscillations and fluctuations around zero. Such trajectories can be viewed as zero-mean functional data. When there are structural breaks in higher-order moments, it is not always easy to spot these by mere visual inspection. Motivated by this challenging problem in brain signal analysis, we propose a detection and testing procedure to find the change point in functional covariance. The detection procedure is based on the cumulative sum statistics (CUSUM). The fully functional testing procedure relies on a null distribution which depends on infinitely many unknown parameters, though in practice only a finite number of these parameters can be included for the hypothesis test of the existence of change point. This paper provides some theoretical insights on the influence of the number of parameters. Meanwhile, the asymptotic properties of the estimated change point are developed. The effectiveness of the proposed method is numerically validated in simulation studies and an application to investigate changes in rat brain signals following an experimentally-induced stroke. © 2022 Board of the Foundation of the Scandinavian Journal of Statistics.

Research Area(s)

  • change point analysis, functional covariance structure, functional data analysis, local field potentials, weakly dependent functional data

Citation Format(s)

Break Point Detection for Functional Covariance. / Jiao, Shuhao; Frostig, Ron D.; Ombao, Hernando.
In: Scandinavian Journal of Statistics, Vol. 50, No. 2, 06.2023, p. 477-512.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review