Before revision:  Moreover, by appealing to the machinery of strong approximations, we accommodate nonparametric settings where estimators of the parameter of interest may not admit asymptotic distributions. We establish asymptotic uniform size control of our test, and characterize classes of alternatives against which it has nontrivial power.
After revision:  Moreover, by appealing to the machinery of strong approximations, our framework accommodates nonparametric regression models as well as distributional/density-related and structural settings.