Discretized normal approximation by Stein's method

DOI10.3150/13-BEJ527zbMath1310.62021arXiv1111.3162MaRDI QIDQ396011

Xiao Fang

Publication date: 8 August 2014

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.3162

zbMATH Keywords

Stein's methodexchangeable pairslocal dependencediscretized normal approximationsize biasingStein couplingStein's approximation

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Characterization and structure theory of statistical distributions (62E10) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items

Non-integrable stable approximation by Stein's method, Multivariate approximation in total variation using local dependence, Multivariate approximation in total variation. I: Equilibrium distributions of Markov jump processes, Multivariate approximation in total variation. II: Discrete normal approximation, Local limit theorems for occupancy models, Normal approximation in total variation for statistics in geometric probability, Approximation of stable law in Wasserstein-1 distance by Stein's method, Error bounds in local limit theorems using Stein's method, Fixed point characterizations of continuous univariate probability distributions and their applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Berry-Esseen bound for the uniform multinomial occupancy model
• Approximation of sums of conditionally independent variables by the translated Poisson distribution
• Zero biasing and a discrete central limit theorem
• Symmetric and centered binomial approximation of sums of locally dependent random variables
• The distribution of leading digits and uniform distribution mod 1
• A central limit theorem for decomposable random variables with applications to random graphs
• On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
• A Berry-Esseen bound with applications to vertex degree counts in the Erdős-Rényi random graph
• Local limit theorems via Landau-Kolmogorov inequalities
• Translated Poisson approximation using exchangeable pair couplings
• Normal Approximation by Stein’s Method
• Poisson perturbations
• An Introduction to Stein's Method
• Multivariate normal approximations by Stein's method and size bias couplings
• The Accuracy of the Gaussian Approximation to the Sum of Independent Variates