Confidence Intervals for Nonparametric Empirical Bayes Analysis

In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization when and why point estimates accurately recover behavior. this paper, develop flexible practical confidence intervals that asymptotic frequentist coverage estimands, such as posterior mean or local false sign rate. The statements hold even estimands are only partially identified converge very slowly. Supplementary materials for article available online.