A general framework for multiple testing dependence.
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.
Leek
Jeffrey T
JT
Department of Oncology, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA.
Storey
John D
JD
D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D012984:Software; D013223:Statistics as Topic