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., 2009, Volume 3, Issue 4,Pages <nobr>41

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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.