Minas, Giorgos (2013) Multivariate global testing and adaptive designs. PhD thesis, University of Warwick.

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Abstract

Global tests are a key research endpoint in multivariate studies. They provide an
omnibus assessment of the overall effects across the multivariate outcomes. This
global evaluation is clearly of high practical value in the field of neuroimaging,
which has become increasingly important in recent years. Existing global testing
methodologies, however, fail to accommodate the demands of neuroimaging studies
that have typically small sample sizes and highly correlated local outcomes.
In this thesis a novel class of multivariate global tests is developed. The
proposed tests are based on a formal framework for using prior information and
accumulated data to learn the effect direction. This framework is used to construct
test statistics that target the estimated effect direction, rather than the whole multivariate
space, for detecting global effects. Adaptive designs are employed to allow for
sequential modifications of the test statistics, based on accumulated data, without
inflating the type I error.
A major focus in our methodology is power performance. The proposed tests
are shown to be optimal in terms of predictive power. Furthermore, a power characterisation
allowing us to explain the behaviour of our tests and perform simple power
analysis is derived. An extensive power analysis, including comparisons to alternative
global tests, is performed. Applications to neuroimaging studies are illustrated
through two real examples. Our results show that the developed methodology can
be particularly useful in cases where the sample sizes are small and prior information
about the effect direction is available.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Multivariate analysis, Experimental design
Official Date:	May 2013
Dates:	Date Event May 2013 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Aston, John A. D.; Stallard, Nigel
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC) (EP/F034210/1)
Extent:	173 leaves : illustrations.
Language:	eng

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