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This article is cited in 21 scientific papers (total in 21 papers)
A New Asymptotic Expansion and Asymptotically Best Constants in Lyapunov's Theorem. I.
G. P. Chistyakov Institute for Low Temperature Physics and Engineering, Ukraine Academy of Sciences
Abstract:
A new asymptotic expansion is obtained in Lyapunov's central limit theorem for distribution functions of centered and normed sums of independent random variables which are not necessarily identically distributed. It is applied to determine the asymptotically best constants in the Berry–Esseen inequality, thus solving problems about their optimal values raised by Kolmogorov and Zolotarev.
Keywords:
central limit theorem, Lyapunov's theorem, Berry–Esseen bounds, asymptotic expansion, characteristic functions.
Received: 30.06.1998
Citation:
G. P. Chistyakov, “A New Asymptotic Expansion and Asymptotically Best Constants in Lyapunov's Theorem. I.”, Teor. Veroyatnost. i Primenen., 46:2 (2001), 326–344; Theory Probab. Appl., 46:2 (2002), 226–242
Linking options:
https://www.mathnet.ru/eng/tvp3921https://doi.org/10.4213/tvp3921 https://www.mathnet.ru/eng/tvp/v46/i2/p326
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