Berry-Esseen bounds in the entropic central limit theorem

DOI10.1007/s00440-013-0510-3zbMath1307.60011arXiv1105.4119OpenAlexW2109433864MaRDI QIDQ398769

Friedrich Götze, Sergey G. Bobkov, Gennadiy P. Chistyakov

Publication date: 15 August 2014

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

Full work available at URL: https://arxiv.org/abs/1105.4119

zbMATH Keywords

entropytotal variationcentral limit theoremBerry-Esseen bounds

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

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Convergence in distribution norms in the CLT for non identical distributed random variables ⋮ Bounds on the Poincaré constant for convolution measures ⋮ A high-dimensional CLT in \(\mathcal {W}_2\) distance with near optimal convergence rate ⋮ The CLT in high dimensions: quantitative bounds via martingale embedding ⋮ Approximation of Markov semigroups in total variation distance under an irregular setting: an application to the CIR process ⋮ On the rate of convergence in the central limit theorem for hierarchical Laplacians ⋮ Rényi divergence and the central limit theorem ⋮ Asymptotic development for the CLT in total variation distance ⋮ On Kac's chaos and related problems ⋮ Existence of Stein kernels under a spectral gap, and discrepancy bounds ⋮ Convergence and asymptotic approximations to universal distributions in probability ⋮ Large ball probabilities, Gaussian comparison and anti-concentration ⋮ Stein's method, logarithmic Sobolev and transport inequalities ⋮ An invariance principle under the total variation distance

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Bounds for characteristic functions in terms of quantiles and entropy
• Upper bounds for minimal distances in the central limit theorem
• Entropy production by block variable summation and central limit theorems
• Entropy and the central limit theorem
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• On the rate of convergence in the entropic central limit theorem
• Fisher information inequalities and the central limit theorem
• Transportation cost for Gaussian and other product measures
• On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
• An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions
• Estimates of the Moments of Sums of Independent Random Variables
• Information theoretic inequalities
• On Convergence in the Mean for Densities
• Refinements of Pinsker's inequality
• A Remark on the Katz-Petrov Theorem

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