Robust Empirical Bayes Confidence Intervals

• 成果类型: Article
• 署名作者: Armstrong, Timothy B.; Kolesar, Michal; Plagborg-Moller, Mikkel
• 署名单位: University of Southern California; Princeton University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA18597
• 发表日期: 2022
• 页码: 2567-2602
• 关键词: false discovery rate; COMPOUND DECISIONS; inference; shrinkage; teachers; impacts

摘要

We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that assume a normal distribution for the means (Morris (1983b)) may substantially undercover when this assumption is violated. In contrast, our EBCIs control coverage regardless of the means distribution, while remaining close in length to the parametric EBCIs when the means are indeed Gaussian. If the means are treated as fixed, our EBCIs have an average coverage guarantee: the coverage probability is at least 1 - alpha on average across the n EBCIs for each of the means. Our empirical application considers the effects of U.S. neighborhoods on intergenerational mobility.