Random subgraph counts and U-statistics: multivariate normal approximation via exchangeable pairs and embedding

DOI10.1239/jap/1276784898zbMath1210.62009arXiv0912.3425OpenAlexW1972644221WikidataQ57747956 ScholiaQ57747956MaRDI QIDQ3578671

Adrian Roellin, Gesine D. Reinert

Publication date: 20 July 2010

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.3425

zbMATH Keywords

Stein's methodmultivariate normal distributionsBernoulli random graphs

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Applications of graph theory (05C90) Random graphs (graph-theoretic aspects) (05C80) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (9)

Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon ⋮ Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance ⋮ Quantitative CLTs for symmetric \(U\)-statistics using contractions ⋮ Moderate deviations of subgraph counts in the Erdős-Rényi random graphs 𝐺(𝑛,𝑚) and 𝐺(𝑛,𝑝) ⋮ Non uniform exponential bounds on normal approximation by Stein’s method and monotone size bias couplings ⋮ Functional approximations via Stein's method of exchangeable pairs ⋮ Stein's method of exchangeable pairs in multivariate functional approximations ⋮ Fixed point characterizations of continuous univariate probability distributions and their applications ⋮ Higher-order fluctuations in dense random graph models

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