April 2021 Only closed testing procedures are admissible for controlling false discovery proportions
Jelle J. Goeman, Jesse Hemerik, Aldo Solari
Author Affiliations +
Ann. Statist. 49(2): 1218-1238 (April 2021). DOI: 10.1214/20-AOS1999


We consider the class of all multiple testing methods controlling tail probabilities of the false discovery proportion, either for one random set or simultaneously for many such sets. This class encompasses methods controlling familywise error rate, generalized familywise error rate, false discovery exceedance, joint error rate, simultaneous control of all false discovery proportions, and others, as well as gene set testing in genomics and cluster inference in neuroimaging. We show that all such methods are either equivalent to a closed testing procedure, or are uniformly improved by one. Moreover, we show that a closed testing method is admissible if and only if all its local tests are admissible. This implies that, when designing methods, it is sufficient to restrict attention to closed testing. We demonstrate the practical usefulness of this design principle by obtaining more informative inferences from the method of higher criticism, and by constructing a uniform improvement of a recently proposed method.


Download Citation

Jelle J. Goeman. Jesse Hemerik. Aldo Solari. "Only closed testing procedures are admissible for controlling false discovery proportions." Ann. Statist. 49 (2) 1218 - 1238, April 2021. https://doi.org/10.1214/20-AOS1999


Received: 1 February 2019; Revised: 1 June 2020; Published: April 2021
First available in Project Euclid: 2 April 2021

Digital Object Identifier: 10.1214/20-AOS1999

Primary: 62F03

Keywords: familywise error rate , higher criticism , multiple testing , selective inference , simultaneous inference

Rights: Copyright © 2021 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.49 • No. 2 • April 2021
Back to Top