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We investigate the convergence rate in the Lyapunov theorem when the third absolute moments exist.
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V. M. Zolotarev (1967), Some inequalities in probability theory and their application in sharpening the Lyapunov theorem. Soviet Math. Dokl., vol. 8, p. 1427-1430
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G. P. Chistyakov (2003), A new asymptotic txpansion and asymptotically best constants in Lyapunov’s theorem. III. Theor. Probab. Appl., vol. 47, no. 3, p. 395-414
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M. Raiñ (2003), Normal approximation by Stein’s method. Proceedings of the Seventh Young Statisticians Meeting. Metodoloski zvezki, vol. 21, p. 71-97
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V. Yu. Korolev, I. G. Shevtsova (2006), On the accuracy of the normal approximation. I. Theor. Probab. Appl., vol. 50, no. 2, p. 298-310
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V. Yu. Korolev, I. G. Shevtsova (2006), On the accuracy of the normal approximation. II. Theor. Probab. Appl., vol. 50, no. 3, p. 473-482
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I. G. Shevtsova (2007), Sharpening of the upper bound of the absolute constant in the Berry-Esseen inequality. Theor. Probab. Appl., vol. 51, no. 3, p. 549-553
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I. S. Shiganov (1986), Refinement of the upper bound of the constant in the central limit theorem. J. Sov. Math., vol. 35, no. 3, p. 2545-2550
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L. Goldstein, G. Reinert (1997), Stein’s method and the zero bias transformation with application to simple random sampling. Ann. Appl. Prob., vol. 7, no. 4, p. 935-952
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Zolotarev V. M., Modern Theory of Summation of Random Variables, VSP, Utrecht, The Netherlands, 1997
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G. P. Chistyakov (2002), A new asymptotic expansion and asymptotically best constants in Lyapunov’s theorem. I. Theor. Probab. Appl., vol. 46, no. 2, p. 226-242
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G. P. Chistyakov (2002), A new asymptotic expansion and asymptotically best constants in Lyapunov’s theorem. II. Theor. Probab. Appl., vol. 46, no. 3, p. 516-522
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I. S. Tyurin, On the convergence rate in Lyapunov’s theorem. Theor. Probab. Appl. (to appear)
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I. S. Tyurin, Refinement of the upper bounds of the constants in Lyapunov’s theorem. Russian Math. Surveys. (to appear)
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2007
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I. S. Tyurin (2009), On the accuracy of the Gaussian approximation. Doklady Akademii Nauk, vol. 429, no. 3, p. 312-316 (English translation: Doklady Mathematics, vol. 80, no. 3)
2009
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V. Yu. Korolev, I. G. Shevtsova (2009), On the upper estimate of the absolute constant in the Berry-Esseen inequality. Theor. Probab. appl., vol. 54, no. 4 (to appear)
2009
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I. G. Shevtsova (2010), Lower asymptotically exact constant in the central limit theorem. Doklady Akademii Nauk, vol. 430., no. 4, p. 1-4 (to appear)
2010
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V. Yu. Korolev, I. G. Shevtsova (2010), An improvement of the Berry-Esseen inequality. Doklady Akademii Nauk, vol. 430. (to appear)
2010
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