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Abstract:
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High-dimensional longitudinal data appear when a large number of variables are measured repeatedly over time. An important challenge of such data is the existence of both spatial and temporal dependence. This paper focuses on testing the temporal homogeneity of covariance matrices in high-dimensional longitudinal data with temporospatial dependence. The data dimension ($p$) is allowed to be much larger than the number of individuals ($n$). A new test statistic is proposed and the asymptotic distribution is established. If the covariance matrices are not homogeneous, an estimator for the location of the change point is given whose rate of convergence is established and shown to depend on $p$, $n$ and the signal-to-noise ratio. The proposed method is extended to estimate multiple change points by applying a binary segmentation approach, which is shown to be consistent under some mild conditions. Simulation studies and an application to a time-course microarray data set are presented to demonstrate the performance of the proposed method.
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