Email this article Esseen–Rozovskii Type Estimates for the Rate of Convergence in the Lindeberg Theorem
- Authors: Gabdullin R.A.1, Makarenko V.1, Shevtsova I.G.2,1,3
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Affiliations:
- Faculty of Computational Mathematics and Cybernetics, Moscow State University
- School of Science, Hangzhou Dianzi University
- Institute of Informatics Problems of Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
- Issue: Vol 234, No 6 (2018)
- Pages: 847-885
- Section: Article
- URL: https://bakhtiniada.ru/1072-3374/article/view/242024
- DOI: https://doi.org/10.1007/s10958-018-4051-2
- ID: 242024
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Abstract
We present structural improvements of Esseen’s (1969) and Rozovskii’s (1974) estimates for the rate of convergence in the Lindeberg theorem and also compute the appearing absolute constants. We introduce the asymptotically exact constants in the constructed inequalities and obtain upper bounds for them. We analyze the values of Esseen’s, Rozovskii’s, and Lyapunov’s fractions, compare them pairwise, and provide some extremal distributions. As an auxiliary statement, we prove a sharp inequality for the quadratic tails of an arbitrary distribution (with finite second-order moment) and its convolutional symmetrization.
About the authors
R. A. Gabdullin
Faculty of Computational Mathematics and Cybernetics, Moscow State University
Email: ishevtsova@cs.msu.ru
Russian Federation, Moscow
V.A. Makarenko
Faculty of Computational Mathematics and Cybernetics, Moscow State University
Email: ishevtsova@cs.msu.ru
Russian Federation, Moscow
I. G. Shevtsova
School of Science, Hangzhou Dianzi University; Faculty of Computational Mathematics and Cybernetics, Moscow State University; Institute of Informatics Problems of Federal Research Center “Computer Science and Control”, Russian Academy of Sciences
Author for correspondence.
Email: ishevtsova@cs.msu.ru
China, Hangzhou; Moscow; Moscow
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