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

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...

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Vydáno v:Scandinavian journal of statistics Ročník 48; číslo 2; s. 375 - 405
Hlavní autoři: Zhong, Ping‐Shou, Li, Jun, Kokoszka, Piotr
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Blackwell Publishing Ltd 01.06.2021
Témata:
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
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Shrnutí: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.
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ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12460