Multiple Testing for Distributional Differences with Non-iid Data

We propose inference methods to compare two continuous distributions across their support, with two main innovations. First, unlike previous such multiple testing procedures, ours apply much more broadly by allowing non-iid sampling, whenever a Donsker's theorem holds. We also establish our procedures' coherence and consonance. Second, we invert these procedures into confidence sets for the set of points where certain (in)equalities hold. For one-sided inference, these points have an economic interpretation in terms of restricted first-order stochastic dominance. All our methods provide much richer results than existing global tests that report only a single "reject" or "not reject" decision.