I. G. Shevtsova, “On the absolute constants in the Berry–Esseen inequality and its structural and nonuniform improvements”, Inform. Primen., 2013, Volume 7, Issue 1,Pages <nobr>124

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

I. G. Shevtsova^ab

^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.