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 Inform. Primen., 2009, Volume 3, Issue 4, Pages 41–56 (Mi ia79)

Asymptotic estimates of the absolute constant in the Berry–Esseen inequality for distribution with unbounded third moment

M. O. Gaponova, I. G. Shevtsova

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

Abstract: The Prawitz' asymptotic estimates for the absolute constant in the Berry–Esseen inequality are sharpened for the case of independent identically distributed random variables with finite third moments. Similar estimates are constructed for the case of unbounded third absolute moment. Also, upper estimates of the asymptotically exact constants in the central limit theorem are presented.

Keywords: central limit theorem; normal approximation; convergence rate estimate; sum of independent random variables; Berry–Esseen inequality; Lyapounov fraction; asymptotically exact constant

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Citation: M. O. Gaponova, I. G. Shevtsova, “Asymptotic estimates of the absolute constant in the Berry–Esseen inequality for distribution with unbounded third moment”, Inform. Primen., 3:4 (2009), 41–56

Citation in format AMSBIB
\Bibitem{GapShe09} \by M.~O.~Gaponova, I.~G.~Shevtsova \paper Asymptotic estimates of the absolute constant in the Berry--Esseen inequality for distribution with unbounded third moment \jour Inform. Primen. \yr 2009 \vol 3 \issue 4 \pages 41--56 \mathnet{http://mi.mathnet.ru/ia79} 

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This publication is cited in the following articles:
1. V. Yu. Korolev, I. G. Shevtsova, “An upper estimate for the absolute constant in the Berry–Esseen inequality”, Theory Probab. Appl., 54:4 (2010), 638–658
2. I. G. Shevtsova, “On the asymptotically exact constants in the Berry–Esseen–Katz inequality”, Theory Probab. Appl., 55:2 (2011), 225–252
3. Korolev V.Yu., Shevtsova I.G., “An improvement of the Berry-Esseen inequalities”, Dokl. Math., 81:1 (2010), 119–123
4. M. E. Grigoreva, I. G. Shevtsova, “Utochnenie neravenstva Katsa–Berri–Esseena”, Inform. i ee primen., 4:2 (2010), 75–82
5. Shevtsova, I.G., “On the accuracy of the normal approximation for sums of independent random variables”, Doklady Mathematics, 85:2 (2012), 274–278
6. Korolev, V., Shevtsova, I., “An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums”, Scandinavian Actuarial Journal, 2012, no. 2, 81–105
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
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