Multivariate analysis of variance and change points estimation for high‐dimensional longitudinal data

• Published in: Scandinavian journal of statistics Vol. 48; no. 2; pp. 375 - 405
• Main Authors: Zhong, Ping‐Shou, Li, Jun, Kokoszka, Piotr
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.06.2021
• Subjects: change points; fMRI data; high‐dimensional means; Homogeneity; longitudinal data; Multivariate analysis; Segmentation; spatial dependence; Statistical tests; temporal dependence; Variance analysis
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/sjos.12460

This article considers the problem of testing temporal homogeneity of p‐dimensional population mean vectors from repeated measurements on n subjects over T times. 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 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.