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2019 Coarse-to-fine multiple testing strategies
Kamel Lahouel, Donald Geman, Laurent Younes
Electron. J. Statist. 13(1): 1292-1328 (2019). DOI: 10.1214/19-EJS1536

Abstract

We analyze control of the familywise error rate (FWER) in a multiple testing scenario with a great many null hypotheses about the distribution of a high-dimensional random variable among which only a very small fraction are false, or “active”. In order to improve power relative to conservative Bonferroni bounds, we explore a coarse-to-fine procedure adapted to a situation in which tests are partitioned into subsets, or “cells”, and active hypotheses tend to cluster within cells. We develop procedures for a non-parametric case based on generalized permutation testing and a linear Gaussian model, and demonstrate higher power than Bonferroni estimates at the same FWER when the active hypotheses do cluster. The main technical difficulty arises from the correlation between the test statistics at the individual and cell levels, which increases the likelihood of a hypothesis being falsely discovered when the cell that contains it is falsely discovered (survivorship bias). This requires sharp estimates of certain quadrant probabilities when a cell is inactive.

Citation

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Kamel Lahouel. Donald Geman. Laurent Younes. "Coarse-to-fine multiple testing strategies." Electron. J. Statist. 13 (1) 1292 - 1328, 2019. https://doi.org/10.1214/19-EJS1536

Information

Received: 1 January 2018; Published: 2019
First available in Project Euclid: 5 April 2019

zbMATH: 07056152
MathSciNet: MR3935850
Digital Object Identifier: 10.1214/19-EJS1536

Subjects:
Primary: 62G10
Secondary: 62G09

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Vol.13 • No. 1 • 2019
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