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

TL;DR

This paper introduces a new statistical test for detecting changes in the mean vectors over time in high-dimensional longitudinal data, accounting for complex dependencies and enabling multiple change-point detection.

Contribution

It proposes a novel test statistic suitable for high-dimensional, temporally dependent data, along with a consistent method for identifying multiple change points.

Findings

The test performs well in simulations under various dependence structures.

The method successfully detects change points in real fMRI data.

Asymptotic distribution is derived under mild conditions.

Abstract

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.