Anytime validity is free: inducing sequential tests

• 成果类型: Article
• 署名作者: Koning, Nick W.; Van Meer, Sam
• 署名单位: Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag050
• 发表日期: 2026-09
• 页码: 1366-1384
• 关键词: anytime validity; E-values; optional continuation; randomized testing; sequential t-test; sequential testing; STUDENTS T-TEST; time-uniform; DESIGN

摘要

Anytime valid sequential tests permit us to stop testing based on the current data, without invalidating the inference. Given a maximum number of observations N, one may believe this must come at the cost of power when compared to a conventional test that waits until all N observations have arrived. Our first contribution is to show that this is false: for any valid test based on N observations, we show how to construct an anytime valid sequential test that matches it after N observations. Our second contribution is that we may use the outcome of a [0,1]-valued test as a conditional significance level in subsequent testing, leading to an overall procedure that is valid at the original significance level. This shows that anytime validity and optional continuation are readily available in traditional testing, without requiring explicit use of e-values. We illustrate this by deriving the anytime valid sequentialized z-test and t-test, which at time N coincide with the traditional z-test and t-test. Finally, we characterize the Sequential Probability Ratio Test by invariance under test induction, and show that it is induced by the Neyman-Pearson test for a tiny level and huge N under an i.i.d. assumption.