Abstract
In the present article, we obtain new explicit estimates for accuracy of approximation in the central limit theorem (CLT). We construct these approximations with the use of asymptotic expansions. We compare the estimates with the real accuracy of approximation for a specific distribution. We also discuss the following question: Why the estimate from the Berry–Esseen theorem cannot catch even the order of proximity of distributions in the CLT?
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Dedicated to A. A. Borovkov on occasion of his 85th birthday
Original Russian Text © V.V. Senatov, 2016, published in Matematicheskie Trudy, 2016, Vol. 19, No. 2, pp. 170–199.
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Senatov, V.V. On the real accuracy of approximation in the central limit theorem. II. Sib. Adv. Math. 27, 133–152 (2017). https://doi.org/10.3103/S1055134417020043
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DOI: https://doi.org/10.3103/S1055134417020043