Safe testing
成果类型：
Article
署名作者：
Pace, Luigi; Salvan, Alessandra
署名单位：
University of Udine; University of Padua
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1093/jrsssb/qkae078
发表日期：
2024
关键词：
摘要：
We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study may depend on previous outcomes. Tests based on e-values are safe, i.e. they preserve type-I error guarantees, under such optional continuation. We define growth rate optimality (GAO) as an analogue of power in an optional continuation context, and we show how to construct GAO e-variables for general testing problems with composite null and alternative, emphasizing models with nuisance parameters. GAO e-values take the form of Bayes factors with special priors. We illustrate the theory using several classic examples including a 1-sample safe t-test and the 2 x 2 contingency table. Sharing Fisherian, Neymanian, and Jeffreys-Bayesian interpretations, e-values may provide a methodology acceptable to adherents of all three schools.
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