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Summary We discover a connection between the Benjamini–Hochberg procedure and the e-Benjamini–Hochberg procedure (Wang & Ramdas, 2022) with a suitably defined set of e-values. This insight extends to Storey’s procedure and generalized versions of the Benjamini–Hochberg procedure and the model-free multiple testing procedure of Barber & Candés (2015) with a general form of rejection rules. We further summarize these findings in a unified form. These connections open up new possibilities for designing multiple testing procedures in various contexts by aggregating e-values from different procedures or assembling e-values from different data subsets.
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Penalized likelihood and multiple testing
Abstract The classical multiple testing model remains an important practical area of statistics with new approaches still being developed. In this paper we develop a new multiple testing procedure inspired by a method sometimes used in a problem with a different focus. Namely, the inference after model selection problem. We note that solutions to that problem are often accomplished by making use of a penalized likelihood function. A classic example is the Bayesian information criterion (BIC) method. In this paper we construct a generalized BIC method and evaluate its properties as a multiple testing procedure. The procedure is applicable to a wide variety of statistical models including regression, contrasts, treatment versus control, change point, and others. Numerical work indicates that, in particular, for sparse models the new generalized BIC would be preferred over existing multiple testing procedures.
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- Award ID(s):
- 1712839
- PAR ID:
- 10461982
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Biometrical Journal
- Volume:
- 61
- Issue:
- 1
- ISSN:
- 0323-3847
- Page Range / eLocation ID:
- p. 62-72
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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