Zero biasing and a discrete central limit theorem

DOI10.1214/009117906000000250zbMath1111.60015arXivmath/0509444OpenAlexW3099506648MaRDI QIDQ858982

Aihua Xia, Larry Goldstein

Publication date: 12 January 2007

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509444

zbMATH Keywords

total variationStein's methodinteger-valued random variables

Mathematics Subject Classification ID

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

Related Items (13)

Kendall's tau-type rank statistics in genome data. ⋮ Geometric sums, size biasing and zero biasing ⋮ Discretized normal approximation by Stein's method ⋮ Normal approximation in total variation for statistics in geometric probability ⋮ Poisson process approximation for dependent superposition of point processes ⋮ On moderate deviations in Poisson approximation ⋮ A polynomial birth-death point process approximation to the Bernoulli process ⋮ Error bounds in local limit theorems using Stein's method ⋮ Translated Poisson approximation using exchangeable pair couplings ⋮ Generalized gamma approximation with rates for urns, walks and trees ⋮ Poisson type approximations for the Markov binomial distribution ⋮ Palm theory, random measures and Stein couplings ⋮ Local limit theorems via Landau-Kolmogorov inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stein's method and point process approximation
• Poisson approximation for dependent trials
• On the binary expansion of a random integer
• Stein's method and the zero bias transformation with application to simple random sampling
• Variational formulas of Poincaré-type inequalities for birth-death processes.
• A non-uniform bound for translated {P}oisson approximation
• Normal approximation for hierarchical structures
• Distributional transformations, orthogonal polynomials, and Stein characterizations
• Stein's method and birth-death processes
• Centered Poisson approximation via Stein's method
• Stein's method, Palm theory and Poisson process approximation.
• Exponential and uniform ergodicity of Markov processes
• \(L^1\) bounds in normal approximation
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
• Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing
• Poisson perturbations
• On the Number of Successes in Independent Trials
• The Accuracy of the Gaussian Approximation to the Sum of Independent Variates

This page was built for publication: Zero biasing and a discrete central limit theorem