Closed testing procedures are classically used for family wise 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.

Goeman, J., Meijer, R., Krebs, T., Solari, A. (2019). Simultaneous control of all false discovery proportions in large-scale multiple hypothesis testing. BIOMETRIKA, 106(4), 841-856 [10.1093/biomet/asz041].

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

Solari A.
2019

Abstract

Closed testing procedures are classically used for family wise 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.
Articolo in rivista - Articolo scientifico
Benjamini-Hochberg procedure; Closed testing; Consonance; False discovery rate; Familywise error rate; Hommel's procedure; Selective inference; Simes test
English
2019
106
4
841
856
reserved
Goeman, J., Meijer, R., Krebs, T., Solari, A. (2019). Simultaneous control of all false discovery proportions in large-scale multiple hypothesis testing. BIOMETRIKA, 106(4), 841-856 [10.1093/biomet/asz041].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/259832
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