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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 2, Pages 345–364
DOI: https://doi.org/10.4213/tvp5097 (Mi tvp5097) 		 
This article is cited in 6 scientific papers (total in 6 papers)

A moment inequality with application to convergence rate estimates in the global CLT for Poisson-binomial random sums

I. G. Shevtsovaabc

a Hangzhou Dianzi University, Zhejiang
b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
c Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (479 kB) Citations (6)
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DOI: https://doi.org/10.4213/tvp5097
Abstract: A moment inequality between the central and noncentral third-order absolute moments is proved, which is optimal for every value of the recentering parameter. By use of this inequality there are constructed convergence rate estimates in the central limit theorem for Poisson-binomial random sums in the uniform and mean metrics.
Keywords: compound Poisson-binomial distribution, central limit theorem (CLT), convergence rate estimate, normal approximation, Berry– Esséen inequality, moment inequality.
Funding agency Grant number
Russian Foundation for Basic Research 15-07-02984а
16-31-60110-мол-а-дк
Ministry of Education and Science of the Russian Federation МД-5642.2015.1
Russian Science Foundation 14-11-00364
The work in Theorem 1 was supported by the Russian Scientific Fund (project 14-11-00364). The rest of the paper was supported by the Grant of the President of Russia MD-5642.2015.1 and by the Russian Foundation for Basic Research (projects 15-07-02984a and 16-31-60110-mol_a_dk).
Received: 15.09.2016
Accepted: 23.02.2017
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 2, Pages 278–294
DOI: https://doi.org/10.1137/S0040585X97T988605
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. G. Shevtsova, “A moment inequality with application to convergence rate estimates in the global CLT for Poisson-binomial random sums”, Teor. Veroyatnost. i Primenen., 62:2 (2017), 345–364; Theory Probab. Appl., 62:2 (2018), 278–294
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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