Journal
STATISTICA SINICA
Volume 31, Issue 2, Pages 959-979Publisher
STATISTICA SINICA
DOI: 10.5705/ss.202018.0027
Keywords
Bump hunting; multiple hypothesis testing; non-identifiability in hypothesis testing; non-nested models comparison
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Funding
- Marie-Skodowska-Curie RISE Grant by the European Commission [H2020MSCA-RISE-2015-691164]
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The study proposes a computationally efficient inferential tool for TOHM, allowing inferences to be made under stringent significance requirements, such as those in the physical sciences, and addressing nonstandard conditions like non-nested model comparisons. It offers a generalized approach to performing inferences under such conditions.
In applied settings, hypothesis testing when a nuisance parameter is identifiable only under the alternative often reduces to a problem of testing one hypothesis multiple times (TOHM). Specifically, a fine discretization of the space of the nonidentifiable parameter is specified, and the null hypothesis is tested against a set of sub-alternative hypotheses, one for each point of the discretization. The resulting sub-test statistics are then combined to obtain a global p-value. We propose a computationally efficient inferential tool to perform TOHM under stringent significance requirements, such as those typically required in the physical sciences, (e.g., a p-value < 10(-7)). The resulting procedure leads to a generalized approach to performing inferences under nonstandard conditions, including non-nested model comparisons.
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