  When are asymptotic approximations using the delta-method uniformly valid? We
provide sufficient conditions as well as closely related necessary conditions
for uniform negligibility of the remainder of such approximations. These
conditions are easily verified and permit to identify settings and parameter
regions where pointwise asymptotic approximations perform poorly. Our framework
allows for a unified and transparent discussion of uniformity issues in various
sub-fields of econometrics. Our conditions involve uniform bounds on the
remainder of a first-order approximation for the function of interest.
