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Inform. Primen., 2013, Volume 7, Issue 1, Pages 124–125 (Mi ia252)  

This article is cited in 9 scientific papers (total in 9 papers)

On the absolute constants in the Berry–Esseen inequality and its structural and nonuniform improvements

I. G. Shevtsovaab

a Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University
b IPI RAN

Abstract: New improved upper bounds are presented for the absolute constants in the Berry–Esseen inequality and its structural and nonuniform improvements. In particular, it is shown that the absolute constant in the classical Berry–Esseen inequality does not exceed 0.5583 in general case and 0.4690 for the case of identically distributed summands. The corresponding bounds in the Nagaev–Bikelis inequality are 21.82 and 17.36.

Keywords: central limit theorem; convergence rate estimate; normal approximation; Berry–Esseen inequality; Nagaev–Bikelis inequality; absolute constant.

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Citation: I. G. Shevtsova, “On the absolute constants in the Berry–Esseen inequality and its structural and nonuniform improvements”, Inform. Primen., 7:1 (2013), 124–125

Citation in format AMSBIB
\Bibitem{She13}
\by I.~G.~Shevtsova
\paper On the absolute constants in~the~Berry--Esseen inequality and~its~structural and~nonuniform improvements
\jour Inform. Primen.
\yr 2013
\vol 7
\issue 1
\pages 124--125
\mathnet{http://mi.mathnet.ru/ia252}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kratz M., “Normex, a New Method For Evaluating the Distribution of Aggregated Heavy Tailed Risks”, Extremes, 17:4 (2014), 661–691  crossref  mathscinet  zmath  isi  scopus
    2. Korolev V.Yu., Smelyanskii R.L., Smelyanskii T.R., Shalimov A.V., “on the Estimation of the Execution Frequency of Sequential Program Code Snippets”, J. Comput. Syst. Sci. Int., 54:4 (2015), 540–545  crossref  mathscinet  isi  elib  scopus
    3. Cundill B., Alexander N.D.E., “Sample Size Calculations For Skewed Distributions”, BMC Med. Res. Methodol., 15 (2015), 28  crossref  isi  elib  scopus
    4. I. G. Shevtsova, “A moment inequality with application to convergence rate estimates in the global CLT for Poisson-binomial random sums”, Theory Probab. Appl., 62:2 (2018), 278–294  mathnet  crossref  crossref  mathscinet  isi  elib
    5. I. Shevtsova, “On the absolute constants in Nagaev-Bikelis-type inequalities”, Inequalities and Extremal Problems in Probability and Statistics: Selected Topics, ed. I. Pinelis, Academic Press Ltd; Elsevier Science Ltd, 2017, 47–102  crossref  mathscinet  isi  scopus
    6. M. Goswami, R. Pagh, F. Silvestri, J. Sivertsen, “Distance sensitive Bloom filters without false negatives”, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, Assoc. Computing Machinery, 2017, 257–269  crossref  mathscinet  zmath  isi
    7. V. Korolev, A. Dorofeeva, “Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions”, Lith. Math. J., 57:1 (2017), 38–58  crossref  mathscinet  zmath  isi  scopus
    8. 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
    9. L. Mattner, J. Schulz, “On normal approximations to symmetric hypergeometric laws”, Trans. Am. Math. Soc., 370:1 (2018), 727–748  crossref  mathscinet  zmath  isi  scopus
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