Resampling-based multi-resolution false discovery exceedance control

2025/09/02 by Hemerik, Jesse · 1 citation
#62G10 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2509.02376

Abstract

MaxT is a highly popular resampling-based multiple testing procedure, which controls the familywise error rate (FWER) and is powerful under dependence. This paper generalizes maxT to what we term ``multi-resolution'' False Discovery eXceedance (FDX) control. FDX control means ensuring that the FDP -- the proportion of false discoveries among all rejections -- is at most γ with probability at least 1-α. Here γ and α are prespecified, small values between 0 and 1. If we take γ=0, FDX control is the same as FWER control. When γ=0, the new procedure reduces to maxT. For γ>0, our method has much higher power. Our method is then strongly connected to maxT as well. For example, if our method rejects fewer than γ^-1 hypotheses, then maxT rejects the same. Further, the implied global tests of the two methods are the same, although the implied closed testing procedures differ. Finally, our method provides an easy-to-use simultaneous, multi-resolution guarantee: the procedure outputs a single rejection threshold q, but ensures that with probability 1-α, simultaneously over all stricter thresholds, the corresponding FDPs are also below γ.

Citations

• Nonparametric methods controlling the median of the false discovery proportion
• Permutation-based multiple testing when fitting many generalized linear models
• SymmPI: Predictive Inference for Data with Group Symmetries
• More Power by using Fewer Permutations
• Asymptotic symmetry and group invariance for randomization
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• Permutation-based true discovery proportions for functional Magnetic Resonance Imaging cluster analysis
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• Efficient computation of adjusted p -values for resampling-based stepdown multiple testing
• Type I error rate control for testing many hypotheses: a survey with proofs

Cited by

• Bringing Closure to False Discovery Rate Control: A General Principle for Multiple Testing

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