Electronic Journal of Statistics

Coarse-to-fine multiple testing strategies

Kamel Lahouel, Donald Geman, and Laurent Younes

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 1292-1328.

Dates
Received: January 2018
First available in Project Euclid: 5 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1554451243

Digital Object Identifier
doi:10.1214/19-EJS1536

Mathematical Reviews number (MathSciNet)
MR3935850

Zentralblatt MATH identifier
07056152

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62G09: Resampling methods

Keywords
Multiple testing FWER hierarchical testing permutation tests

Rights
Creative Commons Attribution 4.0 International License.

Citation

Lahouel, Kamel; Geman, Donald; Younes, Laurent. Coarse-to-fine multiple testing strategies. Electron. J. Statist. 13 (2019), no. 1, 1292--1328. doi:10.1214/19-EJS1536. https://projecteuclid.org/euclid.ejs/1554451243


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