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

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 by high-dimensional longitudinal data, we propose a test statistic that takes into account not only the "large $p$, large $T$ and small $n$" situation, but also the complex temporospatial dependence. The asymptotic distribution of the proposed test statistic is established under mild conditions. When the null hypothesis of temporal homogeneity is rejected, we further propose a binary segmentation method shown to be consistent for multiple change-point identification. Simulation studies and an application to fMRI data are provided to demonstrate the performance of the proposed methods.