High-dimensional multivariate repeated measures analysis with unequal covariance matrices

Solomon W. Harrar, Xiaoli Kong

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In this paper, test statistics for repeated measures design are introduced when the dimension is large. By large dimension is meant the number of repeated measures and the total sample size grow together but either one could be larger than the other. Asymptotic distribution of the statistics is derived for the equal as well as unequal covariance cases in the balanced as well as unbalanced cases. The asymptotic framework considered requires proportional growth of the sample sizes and the dimension of the repeated measures in the unequal covariance case. In the equal covariance case, one can grow at much faster rate than the other. The derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. Consistent and unbiased estimators of the asymptotic variances, which make efficient use of all the observations, are also derived. Simulation study provides favorable evidence for the accuracy of the asymptotic approximation under the null hypothesis. Power simulations have shown that the new methods have comparable power with a popular method known to work well in low-dimensional situation but the new methods have shown enormous advantage when the dimension is large. Data from Electroencephalograph (EEG) experiment is analyzed to illustrate the application of the results.

Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalJournal of Multivariate Analysis
StatePublished - Mar 1 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.


  • Asymptotic
  • Characteristic function
  • Consistency
  • Profile analysis
  • Quadratic form
  • Unequal covariance

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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