Quantitative CLTs for symmetric \(U\)-statistics using contractions

DOI10.1214/19-EJP264zbMath1442.60034arXiv1802.00394OpenAlexW2910165242MaRDI QIDQ1721998

Christian Döbler, Giovanni Peccati

Publication date: 14 February 2019

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

Full work available at URL: https://arxiv.org/abs/1802.00394

zbMATH Keywords

Stein's methoderror boundscentral limit theorem\(U\)-statisticscontractionsrandom geometric graphsexchangeable pairsHoeffding decompositionproduct formula

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Central limit and other weak theorems (60F05) Nonparametric inference (62G99)

Related Items (9)

Berry-Esseen bounds for functionals of independent random variables ⋮ Unnamed Item ⋮ Fourth moment theorems on the Poisson space: analytic statements via product formulae ⋮ Optimal rates for independence testing via $U$-statistic permutation tests ⋮ Stable limit theorems on the Poisson space ⋮ Stein's method of exchangeable pairs in multivariate functional approximations ⋮ The multivariate functional de Jong CLT ⋮ Asymptotic behavior of large Gaussian correlated Wishart matrices ⋮ Functional convergence of sequential \(U\)-processes with size-dependent kernels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic analysis for Poisson point processes. Malliavin calculus, Wiener-Itô chaos expansions and stochastic geometry
• Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences
• Fine Gaussian fluctuations on the Poisson space. I: Contractions, cumulants and geometric random graphs
• Quantitative de Jong theorems in any dimension
• Multi-dimensional Gaussian fluctuations on the Poisson space
• Stein's method and stochastic analysis of Rademacher functionals
• Central limit theorem for integrated square error of multivariate nonparametric density estimators
• A central limit theorem for generalized multilinear forms
• Stein's method and normal approximation of Poisson functionals
• Symmetric statistics, Poisson point processes, and multiple Wiener integrals
• Limit theorems for a triangular scheme of U-statistics with applications to inter-point distances
• Covariances of symmetric statistics
• A class of \(U\)-statistics and asymptotic normality of the number of \(k\)- clusters
• Large sample theory for U-statistics and tests of fit
• On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
• New Berry-Esseen bounds for functionals of binomial point processes
• On the estimation of multiple random integrals and \(U\)-statistics
• Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos
• Fine Gaussian fluctuations on the Poisson space. II: Rescaled kernels, marked processes and geometric \(U\)-statistics
• Normal Approximations with Malliavin Calculus
• On Stein’s method for multivariate normal approximation
• Approximation Theorems of Mathematical Statistics
• Random subgraph counts and U-statistics: multivariate normal approximation via exchangeable pairs and embedding
• Central limit theorems for a class of symmetric statistics
• Random Geometric Graphs
• A Class of Statistics with Asymptotically Normal Distribution
• The Malliavin–Stein Method on the Poisson Space
• Stochastic Analysis for Poisson Processes

This page was built for publication: Quantitative CLTs for symmetric \(U\)-statistics using contractions