Reversing the Berry-Esseen Inequality

DOI10.2307/2044679zbMath0527.60021OpenAlexW4248550471MaRDI QIDQ3042076

Hall, Peter, Andrew David Barbour

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/2044679

zbMATH Keywords

rate of convergencecentral limit theoremlower boundBerry-Esseen inequality

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items (11)

On the normal approximations of \(V\)- and \(L\)-statistics ⋮ Berry-Esseen bounds for Chernoff-type nonstandard asymptotics in isotonic regression ⋮ Effects of design and error on normal convergence rates in regression problems ⋮ A lower bound for the normal approximation of U-statistics ⋮ On a lower bound of the rate of convergence in the central limit theorem for \(m\)-dependent random variables ⋮ Normal approximations for discrete-time occupancy processes ⋮ On a lower bound of \(L_p\) norms in the central limit theorem for \(\varphi\)-mixing random variables ⋮ Stein’s method of normal approximation for dynamical systems ⋮ A lower bound of \(L_p\) norms in the CLT for strongly mixing random variables ⋮ Berry-Esseen bounds in the Breuer-major CLT and Gebelein's inequality ⋮ On the normal approximation of U-statistics of degree two

Cites Work

• Unnamed Item
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
• On the Precision of an Estimate of the Remainder Term in the Central Limit Theorem
• Characterizing the rate of convergence in the central limit theorem. II
• On the Berry-Esseen theorem
• The Accuracy of the Gaussian Approximation to the Sum of Independent Variates

This page was built for publication: Reversing the Berry-Esseen Inequality