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This paper considers the problem of testing temporal homogeneity of$p$-dimensional population mean vectors from the repeated measurements of $n$subjects over $T$ times. To cope with the challenges brought byhigh-dimensional longitudinal data, we propose a test statistic that takes intoaccount not only the "large $p$, large $T$ and small $n$" situation, but alsothe complex temporospatial dependence. The asymptotic distribution of theproposed test statistic is established under mild conditions. When the nullhypothesis of temporal homogeneity is rejected, we further propose a binarysegmentation method shown to be consistent for multiple change-pointidentification. Simulation studies and an application to fMRI data are providedto demonstrate the performance of the proposed methods.

Test for Temporal Homogeneity of Means in High-dimensional Longitudinal Data