Confidence Intervals for Nonparametric Empirical Bayes Analysis

• 成果类型: Article
• 署名作者: Ignatiadis, Nikolaos; Wager, Stefan
• 署名单位: Stanford University; Stanford University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2008403
• 发表日期: 2022
• 页码: 1149-1166
• 关键词: linear functionals; deconvolution; inference; distributions; density; rates

摘要

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.