Before revision:  We show that the maps from marginal distributions to bound functions are not differentiable, but uniform test statistics applied to the bound functions - such as Kolmogorov-Smirnov or Cram\'er-von Mises  - are directionally differentiable.
After revision:  We show that the map from objective function to uniform test statistics applied to the bound functions - such as Kolmogorov-Smirnov or Cram\'er-von Mises - are directionally differentiable.