[{"date_created":"2020-08-17T12:10:55Z","department":[{"_id":"34"},{"_id":"7"},{"_id":"355"}],"type":"preprint","title":"Uniform approximation in classical weak convergence theory","year":"2019","status":"public","date_updated":"2022-01-06T06:53:25Z","user_id":"76599","publication":"arXiv:1903.09864","author":[{"full_name":"Bengs, Viktor","first_name":"Viktor","last_name":"Bengs"},{"first_name":"Hajo","last_name":"Holzmann","full_name":"Holzmann, Hajo"}],"_id":"18018","citation":{"chicago":"Bengs, Viktor, and Hajo 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.","apa":"Bengs, V., & Holzmann, H. (2019). Uniform approximation in classical weak convergence theory. *ArXiv:1903.09864*.","short":"V. Bengs, H. Holzmann, ArXiv:1903.09864 (2019).","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} }","ieee":"V. Bengs and H. Holzmann, “Uniform approximation in classical weak convergence theory,” *arXiv:1903.09864*. 2019.","ama":"Bengs V, Holzmann H. Uniform approximation in classical weak convergence theory. *arXiv:190309864*. 2019."},"abstract":[{"text":"A common statistical task lies in showing asymptotic normality of certain\nstatistics. In many of these situations, classical textbook results on weak\nconvergence theory suffice for the problem at hand. However, there are quite\nsome scenarios where stronger results are needed in order to establish an\nasymptotic normal approximation uniformly over a family of probability\nmeasures. In this note we collect some results in this direction. We restrict\nourselves to weak convergence in $\\mathbb R^d$ with continuous limit measures.","lang":"eng"}]}]