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Detecting Change Points in Multidimensional Functional Data

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Change point detection in sequences of functional data is examined where the functional observations are dependent and where the distributions of change points from multiple subjects is required. Of particular interest is the case where the change point is an epidemic change (a change occurs and then the observations return to baseline at a later time). The special case where the covariance can be decomposed as a tensor product is considered with particular attention to the power analysis for detection. This is of interest in the application to functional magnetic resonance imaging (fMRI), where the estimation of a full covariance structure for the three-dimensional image is not computationally feasible. It is found that use of basis projections such as principal components for detection of the change points can be optimal in situations where PCA is traditionally thought to perform badly. [Joint work with Claudia Kirch, Karlsruhe Institute of Technology]

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