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.
Keywords
Curse of dimensionalityStatistical hypothesis testingKernel (algebra)Multiple comparisons problemSet (abstract data type)Computer scienceStatistical physicsSignificance testingMathematicsStatisticsMachine learningPhysicsCombinatorics
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Publication Info
- Year
- 2008
- Type
- article
- Volume
- 105
- Issue
- 48
- Pages
- 18718-18723
- Citations
- 381
- Access
- Closed
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Cite This
Jeffrey T. Leek,
John D. Storey
(2008).
A general framework for multiple testing dependence.
Proceedings of the National Academy of Sciences
, 105
(48)
, 18718-18723.
https://doi.org/10.1073/pnas.0808709105
Identifiers
- DOI
- 10.1073/pnas.0808709105