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Teor. Veroyatnost. i Primenen., 2010, Volume 55, Issue 2, Pages 271–304 (Mi tvp4201)  

This article is cited in 17 scientific papers (total in 17 papers)

On the asymptotically exact constants in the Berry–Esseen–Katz inequality

I. G. Shevtsova

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

DOI: https://doi.org/10.4213/tvp4201

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English version:
Theory of Probability and its Applications, 2011, 55:2, 225–252

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Received: 15.04.2010

Citation: I. G. Shevtsova, “On the asymptotically exact constants in the Berry–Esseen–Katz inequality”, Teor. Veroyatnost. i Primenen., 55:2 (2010), 271–304; Theory Probab. Appl., 55:2 (2011), 225–252

Citation in format AMSBIB
\by I.~G.~Shevtsova
\paper On the asymptotically exact constants in the Berry--Esseen--Katz inequality
\jour Teor. Veroyatnost. i Primenen.
\yr 2010
\vol 55
\issue 2
\pages 271--304
\jour Theory Probab. Appl.
\yr 2011
\vol 55
\issue 2
\pages 225--252

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    This publication is cited in the following articles:
    1. V. V. Senatov, “On the real accuracy of approximation in the central limit theorem”, Siberian Math. J., 52:4 (2011), 727–746  mathnet  crossref  mathscinet  isi
    2. Yu. S. Nefedova, I. G. Shevtsova, “O tochnosti normalnoi approksimatsii dlya raspredelenii puassonovskikh sluchainykh summ”, Inform. i ee primen., 5:1 (2011), 39–45  mathnet
    3. Nefedova Yu.S., Shevtsova I.G., “Structural improvements of nonuniform convergence rate estimates in the central limit theorem with applications to Poisson random sums”, Dokl. Math., 84:2 (2011), 675–680  crossref  mathscinet  zmath  isi  elib  elib
    4. Yu. S. Nefedova, I. G. Shevtsova, “Nonuniform estimates of convergence rate in the central limit theorem”, Theory Probab. Appl., 57:1 (2013), 28–59  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Shevtsova I.G., “On the accuracy of the normal approximation for sums of independent random variables”, Dokl. Math., 85:2 (2012), 274–278  crossref  mathscinet  zmath  zmath  isi  elib  elib
    6. Shevtsova I.G., “On the accuracy of the normal approximation for sums of symmetric independent random variables”, Dokl. Math., 85:2 (2012), 292–296  crossref  mathscinet  zmath  isi  elib  elib
    7. I. G. Shevtsova, “Moment estimates for the exactness of normal approximation with specified structure for sums of independent symmetrical random variables”, Theory Probab. Appl., 57:3 (2013), 468–496  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. Sunklodas J.K., “Some estimates of normal approximation for the distribution of a sum of a random number of independent random variables”, Lith. Math. J., 52:3 (2012), 326–333  crossref  mathscinet  zmath  isi  elib
    9. I. G. Shevtsova, “On the accuracy of the normal approximation to compound Poisson distributions”, Theory Probab. Appl., 58:1 (2014), 138–158  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. I. G. Shevtsova, “On the absolute constants in the Berry-Esseen-type inequalities”, Dokl. Math., 89:3 (2014), 378–381  crossref  crossref  mathscinet  zmath  zmath  isi  elib
    11. E. L. Maistrenko, “Estimation of the constant in the inequality for the uniform distance between distributions of sequential sums of i.i.d. random variables”, J. Math. Sci. (N. Y.), 229:6 (2018), 741–743  mathnet  crossref  mathscinet
    12. Cekanavicius V., “Approximation Methods in Probability Theory”, Approximation Methods in Probability Theory, Universitext, Springer International Publishing Ag, 2016, 1–274  crossref  mathscinet  isi
    13. Shevtsova I., “On the Absolute Constants in Nagaev-Bikelis-Type Inequalities”, Inequalities and Extremal Problems in Probability and Statistics: Selected Topics, ed. Pinelis I., Academic Press Ltd-Elsevier Science Ltd, 2017, 47–102  crossref  mathscinet  isi
    14. Feng F.Y., Powers M.R., Xiao Rui'an, Zhao L., “Berry-Esseen Bounds For Compound-Poisson Loss Percentiles”, Scand. Actuar. J., 2017, no. 6, 519–534  crossref  mathscinet  zmath  isi
    15. Zolotukhin A. Nagaev S. Chebotarev V., “On a Bound of the Absolute Constant in the Berry-Esseen Inequality For i.i.D. Bernoulli Random Variables”, Mod. Stoch.-THeory Appl., 5:3 (2018), 385–410  crossref  isi
    16. Mattner L. Shevtsova I., “An Optimal Berry-Esseen Type Theorem For Integrals of Smooth Functions”, ALEA-Latin Am. J. Probab. Math. Stat., 16:1 (2019), 487–530  crossref  mathscinet  isi
    17. Shevtsova I. Tselishchev M., “A Generalized Equilibrium Transform With Application to Error Bounds in the Renyi Theorem With No Support Constraints”, Mathematics, 8:4 (2020), 577  crossref  isi
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