In our article, we introduced two general methods for conducting inference for empirical Bayes estimands. The discussants have contributed to our work by clarifying and raising important issues regarding our manuscript, suggesting further applications of empirical Bayes confidence intervals, proposing alternative approaches, and possible extensions. We are grateful to all discussants and the editors for organizing such a stimulating discussion. In our rejoinder, we highlight issues raised by the discussants and give partial answers to some of their questions. In Section 2 we discuss alternative constructions of confidence intervals and provide further context regarding bias-aware inference. In Section 3 we revisit the issue of choosing the class of priors G and in Section 4 we provide more context regarding the empirical Bayes estimands handled by our framework. In Section 5 we analyze Bichsel’s actuarial dataset in more detail with an eye toward grounding some of our preceding points. Finally, in Section 6 we discuss possible improvements and extensions to our methods and in Section 7 we discuss our paper within the broader context of data analysis with empirical Bayes methods. Throughout we refer to equations and sections in the main article as “IW.”
