On the analytical structure of the constant in the nonuniform version of the esseen inequality

DOI10.1080/02331888908802196zbMath0683.60018OpenAlexW2020778101MaRDI QIDQ4733177

Ludwig Paditz

Publication date: 1989

Published in: Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331888908802196

zbMATH Keywords

central limit theoremBerry-Esseen inequalitynonuniform rate of convergence

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05)

Related Items (11)

Normal and poisson approximation of infinitely divisible distribution functions ⋮ The Poisson binomial distribution -- old \& new ⋮ A level-value estimation method and stochastic implementation for global optimization ⋮ On the Error-Bound in the Nonuniform Version of Esseen's Inequality in the L _p -Metric ⋮ Structural improvements of nonuniform convergence rate estimates in the central limit theorem with applications to Poisson random sums ⋮ On convergence rate in CLT for smooth distributions ⋮ An upper bound for the absolute constant in the nonuniform version of the Berry-Esseen inequalities for nonidentically distributed summands ⋮ Non-uniform Berry-Esseen bounds for coordinate symmetric random vectors with applications ⋮ Normal approximation for call function via Stein’s method ⋮ Constants on a Uniform Berry-Esseen Bound on Some Borel Sets in ℝ^kvia Stein's Method ⋮ On the asymptotical behavior of the constant in the Berry-Esseen inequality

Cites Work

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• A nonuniform bound on the rate of convergence in the martingale central limit theorem
• Non-Uniform Estimates, Moderate and Large Deviations in the Central Limit Theorem form-Dependent Random Variables
• [https://portal.mardi4nfdi.de/wiki/Publication:3893039 On the constant in the nonuniform version of the Berry-Ess�en theorem]
• Abschätzungen der Konvergenzgeschwindigkeit zur Normalverteilung unter Voraussetzung einseitiger Momente
• On the Error-Bound in the Nonuniform Version of Esseen's Inequality in the L _p -Metric
• An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality

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