Berry-Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances

DOI10.1007/s00440-017-0756-2zbMath1414.60011OpenAlexW2572853671MaRDI QIDQ681520

Sergey G. Bobkov

Publication date: 12 February 2018

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-017-0756-2

zbMATH Keywords

central limit theoremEdgeworth expansionscouplingtransport distances

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05)

Related Items (12)

Wasserstein-2 bounds in normal approximation under local dependence ⋮ Convergence in distribution norms in the CLT for non identical distributed random variables ⋮ Quadratic transportation cost in the conditional central limit theorem for dependent sequences ⋮ Rates of convergence in the central limit theorem for the elephant random walk with random step sizes ⋮ The Poisson binomial distribution -- old \& new ⋮ Wasserstein-\(p\) bounds in the central limit theorem under local dependence ⋮ The CLT in high dimensions: quantitative bounds via martingale embedding ⋮ A multi-dimensional central limit bound and its application to the euler approximation for Lévy-SDEs ⋮ Equidistribution of random walks on compact groups. II: The Wasserstein metric ⋮ Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes ⋮ Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula ⋮ Stein kernels and moment maps

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