Uniform approximation in classical weak convergence theory

Understand

A common statistical task lies in showing asymptotic normality of certain statistics.

• In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand.
• However, there are quite some scenarios where stronger results are needed in order to establish an asymptotic normal approximation uniformly over a family of probability measures.
• In this note we collect some results in this direction.