Confidence bounds for the true discovery proportion based on the exact distribution of the number of rejections

Friederike Preusse (), Anna Vesely () and Thorsten Dickhaus
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Friederike Preusse: University of Bremen
Anna Vesely: University of Bologna

Annals of the Institute of Statistical Mathematics, 2025, vol. 77, issue 2, No 1, 216 pages

Abstract: Abstract In multiple hypotheses testing it has become widely popular to make inference on the true discovery proportion (TDP) of a set $$\mathscr {M}$$ M of null hypotheses. This approach is useful for several application fields, such as neuroimaging and genomics. Several procedures to compute simultaneous lower confidence bounds for the TDP have been suggested in prior literature. Simultaneity allows for post-hoc selection of $$\mathscr {M}$$ M . If sets of interest are specified a priori, it is possible to gain power by removing the simultaneity requirement. We present an approach to compute lower confidence bounds for the TDP if the set of null hypotheses is defined a priori. The proposed method determines the bounds using the exact distribution of the number of rejections based on a step-up multiple testing procedure under independence assumptions. We assess robustness properties of our procedure and apply it to real data from the field of functional magnetic resonance imaging.

Keywords: Multiple testing; Step-up test; Cluster inference; False discovery proportion; Functional magnetic resonance imaging (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10463-024-00920-x

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