




















Abstract:The literature on hypothesis testing with data-dependent and post-hoc significance levels relies on a particular extension of the Type-I error to data-dependent levels. Existing arguments for this extension are heuristic, and primarily motivated by a resulting connection to the E-value. Our main contribution is to argue that the extension is 'right', by showing that it emerges from three axioms: it is the only extension that nests classical Type-I error validity for data-independent levels, preserves classical validity for data-dependent levels and is monotone in the strength of the rejection claim. We subsequently apply this result to support the common definition of the E-value, by showing that it arises as the 'right' notion of validity for the numerical representation of a generalized hypothesis test that may reject at different data-driven significance levels.
From: Nick Koning [view email]
[v1]
Wed, 27 May 2026 12:59:29 UTC (14 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。