Uniform approximation in classical weak convergence theory

Viktor Bengs; Hajo Holzmann

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arXiv · 1903.09864

Uniform approximation in classical weak convergence theory

Viktor Bengs·Hajo Holzmann

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Abstract

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. We restrict ourselves to weak convergence in $\mathbb R^d$ with continuous limit measures.

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Viktor Bengs, Hajo Holzmann. 2019-03-23. Uniform approximation in classical weak convergence theory. https://arxiv.org/abs/1903.09864

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