2024/11/21 by Anav Sood, Sood, Anav · 1 voice
Computer Science · Mathematics · #Explainable Artificial Intelligence (XAI) #Statistical Methods and Inference #Statistical Methods in Clinical Trials #math.ST #stat.ME
paper · pdf · doi:10.48550/arxiv.2411.13764
openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily perform inference after arbitrary selection procedures. Unlike a traditional p-value, whose distribution must stochastically dominate the uniform distribution under the null, a selectively dominant p-value must have a post-selection distribution that stochastically dominates that of a uniform having undergone the same selection process; moreover, this property must hold simultaneously for all possible selection processes. Despite the strength of this condition, we show that all commonly used p-values (e.g., p-values from two-sided testing in parametric families, one-sided testing in monotone likelihood ratio and exponential families, F-tests for linear regression, and permutation tests) are selectively dominant. By recasting two canonical selective inference problems-inference on winners and rank verification-in our selective dominance framework, we provide simpler derivations, a deeper conceptual understanding, and new generalizations and variations of these methods. Additionally, we use our insights to introduce selective variants of methods that combine p-values, such as Fisher's combination test.