Methods for high-dimensional multivariate and multi-group repeated measures data under non-normality

Abstract

Asymptotic tests for multivariate repeated measures are derived under non-normality and unspecified dependence structure. Notwithstanding their broader scope of application, the methods are particularly useful when a random vector of large number of repeated measurements are collected from each subject but the number of subjects per treatment group is limited. In some experimental situations, replicating the experiment large number of times could be expensive or infeasible. Although taking large number of repeated measurements could be relatively cheaper, due to within subject dependence the number of parameters involved could get large pretty quickly. Under mild conditions on the persistence of the dependence, we have derived asymptotic multivariate tests for the three testing problems in repeated measures analysis. The simulation results provide evidence in favour of the accuracy of the approximations to the null distributions.

Keywords:

• asymptotics
• alpha-mixing
• growth curve
• multivariate tests
• robust methods

Acknowledgments

The authors would like to thank the referees and the associate editor for carefully reading the manuscript and providing valuable comments. The authors are also grateful to the editor for the efficient handling of the manuscript. This publication was partially made possible by a grant from the National Institute of General Medical Sciences (5 U54 GM104944) from the National Institutes of Health.

Disclosure statement

No potential conflict of interest was reported by the authors.