Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 117, Issue 539, Pages 1149-1166Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/01621459.2021.2008403
Keywords
Bias-aware inference; Empirical Bayes; Local false sign rate; Mixture models; Partial identification
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Funding
- Ric Weiland Graduate Fellowship
- National Science Foundation [DMS-1916163]
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In this paper, the authors develop flexible and practical confidence intervals for empirical Bayes estimands. These intervals have asymptotic frequentist coverage, even when the estimands are only partially identified or when empirical Bayes point estimates converge very slowly.
In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of when and why empirical Bayes point estimates accurately recover oracle Bayes behavior. In this paper, we develop flexible and practical confidence intervals that provide asymptotic frequentist coverage of empirical Bayes estimands, such as the posterior mean or the local false sign rate. The coverage statements hold even when the estimands are only partially identified or when empirical Bayes point estimates converge very slowly. for this article are available online.
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