title: Adaptive Multivariate Global Testing.
abstract: We present a methodology for dealing with recent challenges in testing global hypotheses using multivariate observations. The proposed tests target situations, often arising in emerging applications of neuroimaging, where the sample sizenis relatively small compared with the observations' dimensionK. We employ adaptive designs allowing for sequential modifications of the test statistics adapting to accumulated data. The adaptations are optimal in the sense of maximizing the predictive power of the test at each interim analysis while still controlling the Type I error. Optimality is obtained by a general result applicable to typical adaptive design settings. Further, we prove that the potentially high-dimensional design space of the tests can be reduced to a low-dimensional projection space enabling us to perform simpler power analysis studies, including comparisons to alternative tests. We illustrate the substantial improvement in efficiency that the proposed tests can make over standard tests, especially in the case ofnsmaller or slightly larger thanK. The methods are also studied empirically using both simulated data and data from an EEG study, where the use of prior knowledge substantially increases the power of the test. Supplementary materials for this article are available online.
authors.affiliation: Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK.
authors.forename: Giorgos
authors.initials: G
authors.lastname: Minas
authors.affiliation: Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK.
authors.forename: John A D
authors.initials: JA
authors.lastname: Aston
authors.affiliation: Division of Health Sciences, Warwick Medical School, University of Warwick, UK.
authors.forename: Nigel
authors.initials: N
authors.lastname: Stallard
keywords: Adaptive design; Multivariate test; Neuroimaging; Power analysis