Open Access
2019 Accurate inference for repeated measures in high dimensions
Xiaoli Kong, Solomon W. Harrar
Electron. J. Statist. 13(2): 4916-4944 (2019). DOI: 10.1214/19-EJS1644


This paper proposes inferential methods for high-dimensional repeated measures in factorial designs. High-dimensional refers to the situation where the dimension is growing with sample size such that either one could be larger than the other. The most important contribution relates to high-accuracy of the methods in the sense that p-values, for example, are accurate up to the second-order. Second-order accuracy in sample size as well as dimension is achieved by obtaining asymptotic expansion of the distribution of the test statistics, and estimation of the parameters of the approximate distribution with second-order consistency. The methods are presented in a unified and succinct manner that it covers general factorial designs as well as any comparisons among the cell means. Expression for asymptotic powers are derived under two reasonable local alternatives. A simulation study provides evidence for a gain in accuracy and power compared to limiting distribution approximations and other competing methods for high-dimensional repeated measures analysis. The application of the methods are illustrated with a real-data from Electroencephalogram (EEG) study of alcoholic and control subjects.


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Xiaoli Kong. Solomon W. Harrar. "Accurate inference for repeated measures in high dimensions." Electron. J. Statist. 13 (2) 4916 - 4944, 2019.


Received: 1 April 2019; Published: 2019
First available in Project Euclid: 10 December 2019

zbMATH: 07147368
MathSciNet: MR4040758
Digital Object Identifier: 10.1214/19-EJS1644

Primary: 62H10
Secondary: 62H15

Keywords: asymptotic expansion , Characteristic function , Covariance estimation , Multivariate test , profile analysis , quadratic form

Vol.13 • No. 2 • 2019
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