Before revision:  We establish the consistency and weak convergence of nonparametric plug-in estimates of the test statistics and show how they can be used to conduct inference for bounds uniformly over the distribution of treatment effects. We also establish the directional differentiability of minimax operators applied to general - that is , not only convex-concave - functions, which may be of independent interest .
After revision:  We establish the consistency and weak convergence of nonparametric plug-in estimates of the test statistics and show how they can be used to conduct uniform inference. Because the limiting distribution of sample value functions is not generally tractable, to conduct practical inference, we develop detailed resampling techniques that combine a bootstrap procedure with estimates of the directional derivatives .