Simultaneous control of all false discovery proportions in large-scale multiple hypothesis testing

By Jelle J. Goeman, Rosa J. Meijer, Thijmen J. P. Krebs, Aldo Solari. Biometrika, 2016

57 citations recorded by the source corpus.

Closed testing procedures are classically used for familywise error rate control, but they can also be used to obtain simultaneous confidence bounds for the false discovery proportion in all subsets of the hypotheses, allowing for inference robust to post hoc selection of subsets. In this paper we investigate the special case of closed testing with Simes local tests. We construct a novel fast and exact shortcut and use it to investigate the power of this approach when the number of hypotheses goes to infinity. We show that if a minimal level of signal is present, the average power to detect false hypotheses at any desired false discovery proportion does not vanish. Additionally, we show that the confidence bounds for false discovery proportion are consistent estimators for the true false discovery proportion for every nonvanishing subset. We also show close connections between Simes-based closed testing and the procedure of Benjamini and Hochberg.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fea0fece10845ec89f1929f3a0ce81bb1450d2b9

How researchers see this paper

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In Statistics and Probability

1. Jesse Hemerik
2. Aldo Solari
3. Jelle J. Goeman
4. Mark Rubin
5. Anders Gorst-rasmussen
6. Thomas H. Scheike

Citations in the corpus

• Permutation-based simultaneous confidence bounds for the false discovery proportion (2018, methodology): “There we also prove that the method of Goeman and Solari (2011) is equivalent to that in Genovese and Wasserman (2004, 2006).”
• Only closed testing procedures are admissible for controlling false discovery proportions (2019, methodology): “Step-down arguments are standard for FWER control and have been applied to several FDP controlling methods in the past (Blanchard et al., 2017; Goeman et al., 2019; Hemerik et al., 2019).”