Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 105, Issue 48, Pages 18718-18723Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.0808709105
Keywords
empirical null; false discovery rate; latent structure; simultaneous inference; surrogate variable analysis
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Funding
- National Institutes of Health [R01 HG002913]
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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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