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Proc Natl Acad Sci U S A. 2008 Dec 2;105(48):18718-23. doi: 10.1073/pnas.0808709105. Epub 2008 Nov 24.

A general framework for multiple testing dependence.

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  • 1Department of Oncology, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA.

Abstract

We develop a general framework for performing large-scale significance testing in the presence of arbitrarily strong dependence. We derive a low-dimensional set of random vectors, called a dependence kernel, that fully captures the dependence structure in an observed high-dimensional dataset. This result shows a surprising reversal of the "curse of dimensionality" in the high-dimensional hypothesis testing setting. We show theoretically that conditioning on a dependence kernel is sufficient to render statistical tests independent regardless of the level of dependence in the observed data. This framework for multiple testing dependence has implications in a variety of common multiple testing problems, such as in gene expression studies, brain imaging, and spatial epidemiology.

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