New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems
From MaRDI portal
Publication:2117456
DOI10.1214/21-AAP1690zbMath1485.60023arXiv2004.02101OpenAlexW3014314880WikidataQ113752023 ScholiaQ113752023MaRDI QIDQ2117456
Publication date: 21 March 2022
Published in: The Annals of Applied Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2004.02101
Central limit and other weak theorems (60F05) Approximations to statistical distributions (nonasymptotic) (62E17)
Related Items (11)
Berry-Esseen bounds for Chernoff-type nonstandard asymptotics in isotonic regression ⋮ Anti-concentration of polynomials: dimension-free covariance bounds and decay of Fourier coefficients ⋮ High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices ⋮ Stein's method for conditional central limit theorem ⋮ Nearly optimal central limit theorem and bootstrap approximations in high dimensions ⋮ High-dimensional regime for Wishart matrices based on the increments of the solution to the stochastic heat equation ⋮ From \(p\)-Wasserstein bounds to moderate deviations ⋮ Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance ⋮ Covariance representations, \(L^p\)-Poincaré inequalities, Stein's kernels, and high-dimensional CLTs ⋮ Unnamed Item ⋮ Unnamed Item
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Rates of convergence in normal approximation under moment conditions via new bounds on solutions of the Stein equation
- Quantitative de Jong theorems in any dimension
- Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie-Weiss model
- Approximation of rectangular beta-Laguerre ensembles and large deviations
- A central limit theorem for generalized multilinear forms
- Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
- On asymptotic proximity of distributions
- The distribution of leading digits and uniform distribution mod 1
- On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
- Berry-Esseen bounds of normal and nonnormal approximation for unbounded exchangeable pairs
- A smooth transition from Wishart to GOE
- Fourth moment theorems on the Poisson space in any dimension
- From Stein identities to moderate deviations
- Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos
- Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator
- Exchangeable pairs on Wiener chaos
- Stein's method for normal approximation in Wasserstein distances with application to the multivariate central limit theorem
- The CLT in high dimensions: quantitative bounds via martingale embedding
- A multivariate Berry-Esseen theorem with explicit constants
- On the error bound in a combinatorial central limit theorem
- A high-dimensional CLT in \(\mathcal {W}_2\) distance with near optimal convergence rate
- Testing for high-dimensional geometry in random graphs
- On Stein’s method for multivariate normal approximation
- Multidimensional limit theorems for homogeneous sums: A survey and a general transfer principle
- The Berry-Esseen bound for character ratios
- Normal Approximation by Stein’s Method
- Two new proofs of the Erdös–Kac Theorem, with bound on the rate of convergence, by Stein's method for distributional approximations
- Entropic CLT and Phase Transition in High-dimensional Wishart Matrices
- Stein’s method and Plancherel measure of the symmetric group
- The optimal fourth moment theorem
- A Peccati-Tudor type theorem for Rademacher chaoses
This page was built for publication: New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems
