Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences

DOI10.1214/14-AIHP652zbMath1341.60005arXiv1404.0962MaRDI QIDQ297455

Kai Krokowski, Christoph Thäle, Anselm Reichenbachs

Publication date: 27 June 2016

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.0962

zbMATH Keywords

Malliavin calculusStein's methodcentral limit theoremnormal approximationBerry-Esseen boundsRademacher chaosBernoulli random matricesRademacher sequences

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Random matrices (probabilistic aspects) (60B20) Sums of independent random variables; random walks (60G50) Stochastic calculus of variations and the Malliavin calculus (60H07) Random matrices (algebraic aspects) (15B52) Functional limit theorems; invariance principles (60F17)

Related Items (12)

A Peccati-Tudor type theorem for Rademacher chaoses ⋮ Berry-Esseen bounds for functionals of independent random variables ⋮ Spectral integrals of Bernoulli generalized functionals ⋮ Normal approximation for generalizedU-statistics and weighted random graphs ⋮ A simplified second-order Gaussian Poincaré inequality in discrete setting with applications ⋮ Generalized weighted number operators on functionals of discrete-time normal martingales ⋮ Unnamed Item ⋮ Quantitative CLTs for symmetric \(U\)-statistics using contractions ⋮ Stein approximation for functionals of independent random sequences ⋮ Fourth moment theorems on the Poisson space in any dimension ⋮ Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals ⋮ Normal approximation for sums of weighted \(U\)-statistics -- application to Kolmogorov bounds in random subgraph counting

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Normal approximation of Poisson functionals in Kolmogorov distance
• Multi-dimensional Gaussian fluctuations on the Poisson space
• Stein's method and stochastic analysis of Rademacher functionals
• A CLT for a band matrix model
• Stein's method on Wiener chaos
• A new method of normal approximation
• Stein's method and normal approximation of Poisson functionals
• Wiener chaos: Moments, cumulants and diagrams. A survey with computer implementation
• Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
• Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields
• Noise stability of functions with low influences: invariance and optimality
• Multivariate normal approximation using Stein's method and Malliavin calculus
• Stochastic analysis of Bernoulli processes
• A central limit theorem for generalized quadratic forms
• On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
• A central limit theorem for the Poisson-Voronoi approximation
• Rademacher chaos: tail estimates versus limit theorems
• Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos
• Central limit theorems for \(U\)-statistics of Poisson point processes
• Fine Gaussian fluctuations on the Poisson space. II: Rescaled kernels, marked processes and geometric \(U\)-statistics
• Central limit theorems for multiple stochastic integrals and Malliavin calculus
• The Littlewood-Offord problem and invertibility of random matrices
• Smallest singular value of random matrices and geometry of random polytopes
• Central limit theorems for sequences of multiple stochastic integrals
• New Berry-Esseen bounds for non-linear functionals of Poisson random measures
• Universal Gaussian fluctuations of non-Hermitian matrix ensembles: from weak convergence to almost sure CLTs
• Gamma limits and U-statistics on the Poisson space
• Normal Approximations with Malliavin Calculus
• Random Fields on the Sphere
• The exact and asymptotic distribution of overlapping success runs
• Combinatorial Dimension and Certain Norms in Harmonic Analysis
• Moments and Central Limit Theorems for Some Multivariate Poisson Functionals
• The optimal fourth moment theorem

This page was built for publication: Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences