---
_id: '18018'
abstract:
- lang: eng
text: |-
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.
author:
- first_name: Viktor
full_name: Bengs, Viktor
last_name: Bengs
- first_name: Hajo
full_name: Holzmann, Hajo
last_name: Holzmann
citation:
ama: Bengs V, Holzmann H. Uniform approximation in classical weak convergence theory.
*arXiv:190309864*. 2019.
apa: Bengs, V., & Holzmann, H. (2019). Uniform approximation in classical weak
convergence theory. *ArXiv:1903.09864*.
bibtex: '@article{Bengs_Holzmann_2019, title={Uniform approximation in classical
weak convergence theory}, journal={arXiv:1903.09864}, author={Bengs, Viktor and
Holzmann, Hajo}, year={2019} }'
chicago: Bengs, Viktor, and Hajo Holzmann. “Uniform Approximation in Classical Weak
Convergence Theory.” *ArXiv:1903.09864*, 2019.
ieee: V. Bengs and H. Holzmann, “Uniform approximation in classical weak convergence
theory,” *arXiv:1903.09864*. 2019.
mla: Bengs, Viktor, and Hajo Holzmann. “Uniform Approximation in Classical Weak
Convergence Theory.” *ArXiv:1903.09864*, 2019.
short: V. Bengs, H. Holzmann, ArXiv:1903.09864 (2019).
date_created: 2020-08-17T12:10:55Z
date_updated: 2022-01-06T06:53:25Z
department:
- _id: '34'
- _id: '7'
- _id: '355'
publication: arXiv:1903.09864
status: public
title: Uniform approximation in classical weak convergence theory
type: preprint
user_id: '76599'
year: '2019'
...