On the absolute constants in the Berry-Esseen-type inequalities

DOI10.1134/S1064562414030338zbMath1307.60018OpenAlexW2320201772MaRDI QIDQ471399

I. G. Shevtsova

Publication date: 14 November 2014

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562414030338

zbMATH Keywords

central limit theoremBerry-Esseen-type inequalities

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (16)

Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions ⋮ Inferring ground truth from crowdsourced data under local attribute differential privacy ⋮ Berry-Esseen bounds for compound-Poisson loss percentiles ⋮ MAX CUT in weighted random intersection graphs and discrepancy of sparse random set systems ⋮ Bounds for the chi-square approximation of Friedman's statistic by Stein's method ⋮ Estimation of vectors similarity by their randomized binary projections ⋮ Bounds for the Concentration Functions of Random Sums under Relaxed Moment Conditions ⋮ Coalescence on the real line ⋮ Bounds for the accuracy of invalid normal approximation ⋮ Formation of similarity-reflecting binary vectors with random binary projections ⋮ Convergence Rate Estimates in the Global CLT for Compound Mixed Poisson Distributions ⋮ An Estimate for the Sum of the Spitzer Series and Its Generalization ⋮ Fast generation of Gaussian random fields for direct numerical simulations of stochastic transport ⋮ Esseen-Rozovskii type estimates for the rate of convergence in the Lindeberg theorem ⋮ A Moment Inequality with Application to Convergence Rate Estimates in the Global CLT for Poisson-Binomial Random Sums ⋮ Mean estimation and regression under heavy-tailed distributions: A survey

Cites Work

• Unnamed Item
• A square bias transformation of probability distributions: some properties and applications
• On the accuracy of approximation of the complex exponential by the first terms of its Taylor expansion and applications to the Fourier-Stieltjes transform
• Some optimal bounds in the central limit theorem using zero biasing
• Sharpened upper bounds for the absolute constant in the Berry-Esseen inequality for mixed Poisson random sums
• 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 improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums

This page was built for publication: On the absolute constants in the Berry-Esseen-type inequalities