Finding distributions that differ, with false discovery rate control

• 成果类型: Article
• 署名作者: Lee, Yonghoon; Dobriban, Edgar; Tchetgen Tchetgen, Eric J.
• 署名单位: University of Pennsylvania
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asag025
• 发表日期: 2026
• 页码: asag025
• 关键词: Distribution-free inference; False Discovery Rate; Multiple Testing; permutation tests; combination; Consistency

摘要

We consider the problem of comparing a reference distribution with several other distributions. Given a sample from both the reference and the comparison groups, we aim to identify the comparison groups whose distributions differ from that of the reference group. Viewing this as a multiple-testing problem, we introduce a methodology that provides exact, distribution-free control of the false discovery rate. To do so, we introduce the concept of batch conformal p -values and demonstrate that they satisfy positive regression dependence across the groups Benjamini & Yekutieli (2001), thereby enabling control of the false discovery rate through the Benjamini-Hochberg procedure. The proof of positive regression dependence introduces a novel technique for the inductive construction of rank vectors with almost-sure dominance under exchangeability. We evaluate the performance of the proposed procedure through simulations. Despite being distribution-free, in some cases it shows performance comparable to methods with knowledge of the data-generating normal distribution, and it further has more power than direct approaches based on conformal out-of-distribution detection. Furthermore, we illustrate our methods on a hepatitis C treatment dataset, where they identify patient groups with large treatment effects, and on the Current Population Survey dataset, where they identify subpopulations with long working hours.