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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 2, Pages 345–364 (Mi tvp5097)  

This article is cited in 3 scientific papers (total in 3 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

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


DOI: https://doi.org/10.4213/tvp5097

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English version:
Theory of Probability and its Applications, 2018, 62:2, 278–294

Bibliographic databases:

Received: 15.09.2016
Accepted:23.02.2017

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. Shevtsova, “On the absolute constants in Nagaev-Bikelis-type inequalities”, Inequalities and extremal problems in probability and statistics, Academic Pres, London, 2017, 47–102  crossref  mathscinet  isi
    2. I. G. Shevtsova, “Convergence rate estimates in the global CLT for compound mixed Poisson distributions”, Theory Probab. Appl., 63:1 (2018), 72–93  mathnet  crossref  crossref  isi  elib
    3. V. Yu. Korolev, A. V. Dorofeeva, “O neravnomernykh otsenkakh tochnosti normalnoi approksimatsii dlya raspredelenii nekotorykh sluchainykh summ pri oslablennykh momentnykh usloviyakh”, Inform. i ee primen., 12:4 (2018), 86–91  mathnet  crossref  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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