General Bahr-Esseen inequalities and their applications

We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent p if it holds with exponent [Formula: see text] for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply th...

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Autores principales: Fazekas, István, Pecsora, Sándor
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5562838/
https://www.ncbi.nlm.nih.gov/pubmed/28867922
http://dx.doi.org/10.1186/s13660-017-1468-y
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author Fazekas, István
Pecsora, Sándor
author_facet Fazekas, István
Pecsora, Sándor
author_sort Fazekas, István
collection PubMed
description We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent p if it holds with exponent [Formula: see text] for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply the results to obtain weak and strong laws of large numbers and complete convergence.
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spelling pubmed-55628382017-09-01 General Bahr-Esseen inequalities and their applications Fazekas, István Pecsora, Sándor J Inequal Appl Research We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent p if it holds with exponent [Formula: see text] for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply the results to obtain weak and strong laws of large numbers and complete convergence. Springer International Publishing 2017-08-18 2017 /pmc/articles/PMC5562838/ /pubmed/28867922 http://dx.doi.org/10.1186/s13660-017-1468-y Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Fazekas, István
Pecsora, Sándor
General Bahr-Esseen inequalities and their applications
title General Bahr-Esseen inequalities and their applications
title_full General Bahr-Esseen inequalities and their applications
title_fullStr General Bahr-Esseen inequalities and their applications
title_full_unstemmed General Bahr-Esseen inequalities and their applications
title_short General Bahr-Esseen inequalities and their applications
title_sort general bahr-esseen inequalities and their applications
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5562838/
https://www.ncbi.nlm.nih.gov/pubmed/28867922
http://dx.doi.org/10.1186/s13660-017-1468-y
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