Title: MANOVA and change points estimation for high-dimensional longitudinal data
Authors: Ping-Shou Zhong - University of Illinois at Chicago (United States) [presenting]
Jun Li - Kent State University (United States)
Piotr Kokoszka - Colorado State University (USA)
Abstract: The problem of testing temporal homogeneity of $p$-dimensional population mean vectors from repeated measurements on $n$ subjects over $T$ times is considered. To cope with the challenges brought about by high dimensional longitudinal data, we propose methodology that takes into account not only the ``large $p$, large $T$ and small $n$'' situation, but also the complex temporospatial dependence. We consider both the multivariate analysis of variance (MANOVA) problem and the change point problem. The asymptotic distributions of the proposed test statistics are established under mild conditions. In the change point setting, when the null hypothesis of temporal homogeneity is rejected, we further propose a binary segmentation method and show that it is consistent with a rate that explicitly depends on $p$, $T$ and $n$. Simulation studies and an application to fMRI data are provided to demonstrate the performance and applicability of the proposed methods.