AI Insight
This paper presents a novel statistical framework for combining evidence from multiple tests when the dependence structure between them is unknown or complex. The method uses permutation-based transformations to create exchangeable datasets, then aggregates evidence across these transformations while maintaining statistical validity. The authors prove that their approach uniformly outperforms traditional conservative methods like Bonferroni correction while automatically adapting to the actual dependence structure in the data.
Why it matters
The framework addresses a fundamental challenge in statistics where researchers need to combine results from multiple related tests but cannot assume independence. Applications to nonparametric testing and conformal prediction demonstrate practical improvements over existing methods, potentially enabling more powerful and flexible statistical inference across diverse scientific domains where complex dependencies are common.
Understand the Science
arXiv:2607.15823v1 Announce Type: cross
Abstract: We study aggregation of statistical evidence under unknown and potentially complex dependence using group-invariance. Building on permutation-based constructions that treat transformed datasets as exchangeable units, we aggregate evidence across statistics for each transformed dataset and calibrate the resulting aggregates across transformations. We develop a finite-sample power and adaptivity theory for this framework, together with extensions to sequential and data-dependent aggregation that preserve validity. For single-batch aggregation, which uses one collection of transformed datasets for both standardization and calibration, we show that the critical values uniformly improve on deterministic calibrations valid under arbitrary dependence, including Bonferroni correction, while adapting to the unknown dependence structure. We also introduce a sequential alpha-spending version that permits early rejection when evidence is strong, and a two-batch extension that separates standardization from calibration to accommodate learned aggregation rules and reduce computation. Applications to adaptive nonparametric testing and conformal prediction illustrate how these results sharpen existing aggregation methods.
Source: Aggregation of Statistical Evidence under Exchangeability