Abstract
This paper considers Bayesian multiple testing under sparsity for polynomial-tailed distributions satisfying a monotone likelihood ratio property. Included in this class of distributions are the Student's t, the Pareto, and many other distributions. We prove some general asymptotic optimality results under fixed and random thresholding. As examples of these general results, we establish the Bayesian asymptotic optimality of several multiple testing procedures in the literature for appropriately chosen false discovery rate levels. We also show by simulation that the Benjamini-Hochberg procedure with a false discovery rate level different from the asymptotically optimal one can lead to high Bayes risk.
Original language | English (US) |
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Pages (from-to) | 1225-1242 |
Number of pages | 18 |
Journal | Statistica Sinica |
Volume | 27 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2017 |
Externally published | Yes |
Keywords
- Asymptotic optimality
- Benjamini-Hochberg procedure
- False discovery rate
- Pareto distribution
- Student's t distribution
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty