# Confidence Intervals for Nonparametric Empirical Bayes Analysis

## TL;DR

This paper develops practical confidence intervals for empirical Bayes estimands that guarantee asymptotic frequentist coverage, even under partial identification or slow convergence of point estimates.

## Contribution

It introduces flexible confidence intervals for empirical Bayes analysis that ensure coverage despite partial identification or slow convergence.

## Key findings

- Confidence intervals achieve asymptotic frequentist coverage.
- Coverage holds even with partial identification.
- Method is robust to slow convergence of point estimates.

## Abstract

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.