JRSSB Jul 31, 2026

False discovery rate control with compound p-values

Authors
Rina Foygel Barber Richard J Samworth
Research Topics
Hypothesis Testing
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Paper Information
  • Journal:
    Journal of the Royal Statistical Society Series B
  • DOI:
    10.1093/jrsssb/qkag116
  • Published:
    July 31, 2026
  • Added to Tracker:
    Aug 03, 2026
Abstract

Abstract In the setting of multiple testing, compound p-values generalize p-values by asking for superuniformity to hold only on average across all true nulls. We study the properties of the Benjamini–Hochberg procedure applied to compound p-values. Under independence, we show that the false discovery rate (FDR) is at most 1.93α, where α is the nominal level, and exhibit a distribution for which the FDR is 76α. If additionally all nulls are true, then the upper bound can be improved to α+2α2, with a corresponding worst-case lower bound of α+α2/4. Under positive dependence, on the other hand, we demonstrate that FDR can be inflated by a factor of O(logm), where m is the number of hypotheses. We provide numerous examples of settings where compound p-values arise in practice, either because we lack sufficient information to compute non-trivial p-values, or to facilitate a more powerful analysis.

Author Details
Rina Foygel Barber
Author
Richard J Samworth
Author
Research Topics & Keywords
Hypothesis Testing
Research Area
Citation Information
APA Format
Rina Foygel Barber & Richard J Samworth (2026) . False discovery rate control with compound p-values. Journal of the Royal Statistical Society Series B , 10.1093/jrsssb/qkag116.
BibTeX Format
@article{paper1491,
  title = { False discovery rate control with compound p-values },
  author = { Rina Foygel Barber and Richard J Samworth },
  journal = { Journal of the Royal Statistical Society Series B },
  year = { 2026 },
  doi = { 10.1093/jrsssb/qkag116 },
  url = { https://doi.org/10.1093/jrsssb/qkag116 }
}
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