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Mathematics > Statistics Theory
Title: Safe Testing
(Submitted on 18 Jun 2019 (v1), last revised 10 Mar 2023 (this version, v5))
Abstract: 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 (GRO) as an analogue of power in an optional continuation context, and we show how to construct GRO e-variables for general testing problems with composite null and alternative, emphasizing models with nuisance parameters. GRO e-values take the form of Bayes factors with special priors. We illustrate the theory using several classic examples including a one-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.
Submission history
From: Rianne de Heide [view email][v1] Tue, 18 Jun 2019 20:39:27 GMT (85kb,D)
[v2] Wed, 10 Jun 2020 08:38:35 GMT (96kb,D)
[v3] Mon, 6 Dec 2021 20:41:47 GMT (75kb,D)
[v4] Tue, 7 Mar 2023 15:17:24 GMT (165kb,D)
[v5] Fri, 10 Mar 2023 13:14:45 GMT (165kb,D)
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