Bringing Closure to False Discovery Rate Control: A General Principle for Multiple Testing
Ziyu Xu, Aldo Solari, Lasse Fischer, Rianne de Heide, Aaditya Ramdas, and Jelle Goeman
Bringing Closure to False Discovery Rate Control: A General Principle for Multiple Testing
Ziyu Xu, Aldo Solari, Lasse Fischer, Rianne de Heide, Aaditya Ramdas, and Jelle Goeman
arXiv, 2025 software: R (eClosure) Python (eclosure)
This work subsumes: The e-Partitioning Principle of False Discovery Rate Control
Jelle Goeman, Rianne de Heide and Aldo Solari
Arxiv, 2025, submitted
What is this paper about?
This preprint develops a closure principle for error criteria based on expected loss, including the false discovery rate. It shows that existing FDR procedures can be viewed through this framework, derives systematic improvements and explains why closure naturally gives simultaneous and post-hoc guarantees.
Summary
We present a necessary and sufficient principle for multiple-testing methods that control an expected loss. Every such method can be represented as a general closed testing procedure based on e-values. This extends the classical closure principle beyond familywise error and tail probabilities of the false discovery proportion to a broad class of error rates, including the false discovery rate. Existing procedures such as e-BH and Benjamini–Yekutieli can be written as special cases, which leads to uniform improvements. The closure perspective also yields simultaneous validity over many rejected sets and allows several kinds of post-hoc flexibility, including in the choice of error metric and, under conditions, the nominal level.