Title

Robust Empirical Bayes Confidence Intervals

Author(s)

Timothy B. Armstrong Timothy Armstrong (University of Southern California)

Michal Kolesár Michal Kolesár (Princeton University)

Mikkel Plagborg-Møller Mikkel Plagborg-Møller (Princeton University)

Abstract

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−α on average across the n EBCIs for each of the means. Our empirical application considers the effects of U.S. neighborhoods on intergenerational mobility.

Creation Date

2022-05

Section URL ID

Paper Number

2022-27

URL

https://www.princeton.edu/~mkolesar/papers/ebci.pdf

File Function

Jel

C11, C14, C18

Keyword(s)

average coverage, empirical Bayes, confidence interval, shrinkage

Suppress

false

Series

13