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.

翻译：我们用一个正常的手段问题构建了强大的实验性贝ys信任间隔(EBCIs ) 。 间隔以通常的线性贝耶斯测算器为中心, 但使用临界值来计算收缩。 假设手段正常分配的参数 ELBIs( Morris, 1983年b) 可能在这一假设被违反时基本上处于地下。 相反, 我们的EBCIs 控制范围无论手段分配如何,而当手段确实为Gaussian时则与参数 EBCIs 保持距离很近。 如果手段是固定的, 我们的EBCIs有一个平均覆盖率保证:在每种手段的EBCIs中平均覆盖概率至少为1美元 - 阿尔法元。 我们的经验应用考虑了美国居民区对代际流动性的影响。