Admissible ways of merging p-values under arbitrary dependence

2022/02/01 by Vladimir Vovk, Bin Wang, Ruodu Wang · 38 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Mathematics #Optimal Experimental Design Methods #Representation (politics) #Statistical Methods in Clinical Trials #Statistics #Value (mathematics)

paper · doi:10.1214/21-aos2109

published in The Annals of Statistics 50(1) (Institute of Mathematical Statistics)

openalex publication_date 2022/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Methods of merging several p-values into a single p-value are important in their own right and widely used in multiple hypothesis testing. This paper is the first to systematically study the admissibility (in Wald’s sense) of p-merging functions and their domination structure, without any information on the dependence structure of the input p-values. As a technical tool, we use the notion of e-values, which are alternatives to p-values recently promoted by several authors. We obtain several results on the representation of admissible p-merging functions via e-values and on (in)admissibility of existing p-merging functions. By introducing new admissible p-merging functions, we show that some classic merging methods can be strictly improved to enhance power without compromising validity under arbitrary dependence.

Citations

• Calibration ofρValues for Testing Precise Null Hypotheses

Cited by

• Admissibility and Complete Classes for False Discovery Rate Control with E-values
• Hypothesis Testing with E-values
• Gaffke's confidence interval for the mean of bounded data is inadmissible but asymptotically efficient
• Priority-preserving augmentation of goodness-of-fit tests by conditional calibration
• Symmetric Aggregation of Conformity Scores for Efficient Uncertainty Sets
• Extended Convolution Bounds on the Fréchet Problem: Robust Risk Aggregation and Risk Sharing
• Elements of Conformal Prediction for Statisticians
• E-Scores for (In)Correctness Assessment of Generative Model Outputs
• False discovery rate control with e-values
• Bringing Closure to False Discovery Rate Control: A General Principle for Multiple Testing
• Class conditional conformal prediction for multiple inputs by p-value aggregation
• Valid and efficient possibilistic fusion
• The e-Partitioning Principle of False Discovery Rate Control

Related

• Admissible ways of merging p-values under arbitrary dependence
• Trade-off between validity and efficiency of merging p-values under arbitrary dependence
• A simple geometric proof for the characterisation of e-merging functions
• The only admissible way of merging arbitrary e-values
• Combining p-values via averaging