Break point detection for functional covariance

Shuhao Jiao, Ron D. Frostig, Hernando Ombao

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish (US)
JournalScandinavian Journal of Statistics
DOIs
StatePublished - Apr 18 2022

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'Break point detection for functional covariance'. Together they form a unique fingerprint.

Cite this