  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.
