On natural convergence rate estimates in the Lindeberg theorem

Ruslan Gabdullin; Vladimir Makarenko; Irina Shevtsova

doi:10.1007/s13171-020-00206-3

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arXiv · 1912.12091

On natural convergence rate estimates in the Lindeberg theorem

Ruslan Gabdullin·Vladimir Makarenko·Irina Shevtsova

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Abstract

We prove two estimates of the rate of convergence in the Lindeberg theorem, involving algebraic truncated third-order moments and the classical Lindeberg fraction, which generalize a series of inequalities due to (Esseen, 1969), (Rozovskii, 1974), (Wang, Ahmad, 2016), some of our recent results in (Gabdullin, Makarenko, Shevtsova, 2018, 2019) and, up to constant factors, also (Katz, 1963), (Petrov, 1965), (Osipov, 1966). The technique used in the proof is completely different from that in (Wang, Ahmad, 2016) and is based on some extremal properties of introduced fractions which has not been noted in (Katz, 1963), (Petrov, 1965), (Wang, Ahmad, 2016).

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Ruslan Gabdullin, Vladimir Makarenko, Irina Shevtsova. 2019-12-27. On natural convergence rate estimates in the Lindeberg theorem. https://doi.org/10.1007/s13171-020-00206-3

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