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An optimal Berry-Esseen type inequality for expectations of smooth functions. (English. Russian original) Zbl 1381.60066
Dokl. Math. 95, No. 3, 250-253 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 474, No. 5, 535-539 (2017).
From the abstract: In this brief, purely mathematical note, the authors provide an optimal Berry-Esseen type inequality for Zolotarev’s ideal \(\zeta_3\)-metric measuring the difference between expectations of sufficiently smooth functions of a sum of independent random variables \(X_1,\dots,X_n\) with finite third-order moments and a sum of independent symmetric two-point random variables \(Y_i\), isoscedastic to the \(X_i\). This improves an earlier result by I. S. Tyurin [Dokl. Math. 80, No. 3, 840–843 (2009; Zbl 1201.60018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 429, No. 3, 312–316 (2009)].

MSC:
60E15 Inequalities; stochastic orderings
60E05 Probability distributions: general theory
62E15 Exact distribution theory in statistics
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References:
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