Best possible bounds of the von Bahr--Esseen type
نویسندگان
چکیده
منابع مشابه
General Bahr-Esseen inequalities and their applications
We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent p if it holds with exponent [Formula: see text] for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply the results to obtain weak and strong laws of large numbers and complete convergence.
متن کاملErratum to: General Bahr-Esseen inequalities and their applications
*Correspondence: [email protected] Faculty of Informatics, University of Debrecen, P.O. Box 400, Debrecen, 4002, Hungary 1 Erratum In the publication of this article [], there were two errors. ) The error in Section . Exponential inequalities and their consequences: ‘(a)X(b) = –aI{X < a} +XIa≤ |X| ≤ b + bI{X > b}.’ Should instead read: ‘(a)X(b) = aI{X < a} +XIa≤ X ≤ b + bI{X > b}...
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Best possible lower bounds on the coefficients of Ehrhart polynomials
For an integral convex polytope P ⊂ R, we recall i(P, n) = |nP∩Z|the Ehrhart polynomial of P. Let for r = 0, . . . , d,gr(P) be the r-th coefficients ofi(P, n). Martin Henk and Makoto Tagami gave the lower bounds on the coefficientsgr(P) in terms of the volume of P. In general, these bounds are not best possible.However, it is known that in the cases r ∈ {1, 2, d − 2}, these...
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We derive uniform and non–uniform error bounds in the normal approximation under a general dependence assumption. Our method is tailor made for dynamic time series models employed in the econometric literature but it is also applicable for many other dependent processes. Neither stationarity nor any smoothness conditions of the underlying distributions are required. If the introduced weak depen...
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ژورنال
عنوان ژورنال: Annals of Functional Analysis
سال: 2015
ISSN: 2008-8752
DOI: 10.15352/afa/06-4-1