On the asymptotical behavior of the constant in the Berry-Esseen inequality

DOI10.1007/BF02214268zbMath0799.60019MaRDI QIDQ1322906

Vidmantas Bentkus

Publication date: 17 November 1994

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

zbMATH Keywords

universal constantasymptotic of the constantBerry-Esséen estimate

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items

On Hoeffding's inequalities. ⋮ The lower asymptotically exact constant in the central limit theorem ⋮ Self-normalized Cramér-type large deviations for independent random variables. ⋮ Shortening the distance between Edgeworth and Berry-Esseen in the classical case ⋮ On the accuracy of the normal approximation for sums of independent random variables ⋮ On the accuracy of the normal approximation for sums of symmetric independent random variables ⋮ An optimal Berry-Esseen type theorem for integrals of smooth functions ⋮ Poisson limit theorems for number of given value cells in non-homogeneous generalized allocation scheme ⋮ Asymptotically proper constants in the Lyapunov theorem ⋮ An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums

Cites Work

• Estimates of the proximity of a distribution to the normal law
• [https://portal.mardi4nfdi.de/wiki/Publication:3893039 On the constant in the nonuniform version of the Berry-Ess�en theorem]
• Weitere Ungleichungen für den absoluten Betrag einer charakteristischen Function
• On the remainder in the central limit theorem
• On the analytical structure of the constant in the nonuniform version of the esseen inequality
• An Absolute Estimate of the Remainder Term in the Central Limit Theorem
• Bounds for the Central Limit Theorem Error
• An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality
• The Extrema of the Expected Value of a Function of Independent Random Variables
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