Abstract
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.
Original language | English (US) |
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Pages (from-to) | 959-979 |
Number of pages | 21 |
Journal | Statistica Sinica |
Volume | 31 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2021 |
Bibliographical note
Publisher Copyright:© 2021 Institute of Statistical Science. All rights reserved.
Keywords
- Bump hunting
- Multiple hypothesis testing
- Non-identifiability in hypothesis testing
- Non-nested models comparison