Rates of convergence for multivariate normal approximation with applications to dense graphs and doubly indexed permutation statistics

DOI10.3150/14-BEJ639zbMath1344.60024arXiv1206.6586OpenAlexW3098134439MaRDI QIDQ888478

Xiao Fang, Adrian Roellin

Publication date: 30 October 2015

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.6586

zbMATH Keywords

Stein's methodrandom graphspermutation statisticsdense graph limitsmultivariate normal approximationnon-smooth metrics

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random graphs (graph-theoretic aspects) (05C80)

Related Items (8)

Multivariate approximation in total variation. II: Discrete normal approximation ⋮ Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon ⋮ Rates of multivariate normal approximation for statistics in geometric probability ⋮ From \(p\)-Wasserstein bounds to moderate deviations ⋮ A multivariate CLT for bounded decomposable random vectors with the best known rate ⋮ Multivariate second order Poincaré inequalities for Poisson functionals ⋮ Berry-Esseen bounds in the inhomogeneous Curie-Weiss model with external field ⋮ Higher-order fluctuations in dense random graph models

Cites Work

• Unnamed Item
• Unnamed Item
• Convergent sequences of dense graphs. II. Multiway cuts and statistical physics
• A multivariate CLT for decomposable random vectors with finite second moments
• On the rate of convergence in the multivariate CLT
• The asymptotic distributions of generalized U-statistics with applications to random graphs
• Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing
• Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
• Stein's method for diffusion approximations
• Representations for partially exchangeable arrays of random variables
• A central limit theorem for decomposable random variables with applications to random graphs
• The reverse isoperimetric problem for Gaussian measure
• Error bound in a central limit theorem of double-indexed permutation statistics
• On the dependence of the Berry-Esseen bound on dimension
• A multivariate CLT for local dependence with \(n^{-1/2}\log n\) rate and applications to multivariate graph related statistics
• Finitely forcible graphons
• Combinatorics of partial derivatives
• Graph limits and exchangeable random graphs
• Metrics for sparse graphs
• Multivariate normal approximations by Stein's method and size bias couplings
• Quasi-random graphs

This page was built for publication: Rates of convergence for multivariate normal approximation with applications to dense graphs and doubly indexed permutation statistics