Break Point Detection for Functional Covariance
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Many experiments record sequential trajectories that oscillate around zero. Such trajectories can be viewed as zero-mean functional data. When there are structural breaks (on the sequence of curves) in higher order moments, it is often difficult to spot these by mere visual inspection. Thus, we propose a detection and testing procedure to find the change-points in functional covariance. The method is fully functional in the sense that no dimension reduction is needed. We establish the asymptotic properties of the estimated change-point. The effectiveness of the proposed method is numerically validated in the simulation studies and an application to study structural changes in rat brain signals in a stroke experiment.
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