Normal approximation for sums of weighted \(U\)-statistics -- application to Kolmogorov bounds in random subgraph counting

DOI10.3150/19-BEJ1141zbMath1464.60021arXiv1806.05339OpenAlexW2990785190MaRDI QIDQ2278673

Nicolas Privault, Grzegorz Serafin

Publication date: 5 December 2019

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05339

zbMATH Keywords

central limit theoremKolmogorov distancerandom graphnormal approximationBerry-Esseen boundStein-Chen methodsubgraph countMalliavin-Stein method

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random graphs (graph-theoretic aspects) (05C80) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (7)

KOLMOGOROV BOUNDS FOR THE NORMAL APPROXIMATION OF THE NUMBER OF TRIANGLES IN THE ERDŐS–RÉNYI RANDOM GRAPH ⋮ Berry-Esseen bounds for functionals of independent random variables ⋮ Normal approximation for generalizedU-statistics and weighted random graphs ⋮ Kolmogorov bounds for decomposable random variables and subgraph counting by the Stein-Tikhomirov method ⋮ A simplified second-order Gaussian Poincaré inequality in discrete setting with applications ⋮ Higher-order fluctuations in dense random graph models ⋮ Berry-Esseen bounds for generalized \(U\)-statistics

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