High-dimensional central limit theorems by Stein's method
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Publication:2240863
DOI10.1214/20-AAP1629zbMath1476.60049arXiv2001.10917OpenAlexW3200683718WikidataQ113752027 ScholiaQ113752027MaRDI QIDQ2240863
Publication date: 4 November 2021
Published in: The Annals of Applied Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2001.10917
Stein's methodcentral limit theoremmultiple Wiener-Itô integralshigh dimensionsexchangeable pairslocal dependenceStein kernelnonlinear statistic
Central limit and other weak theorems (60F05) Approximations to statistical distributions (nonasymptotic) (62E17)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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- Unnamed Item
- Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem
- Log-concavity and strong log-concavity: a review
- Statistics for high-dimensional data. Methods, theory and applications.
- On the rate of convergence in the multivariate CLT
- Stein's method on Wiener chaos
- Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space
- A new method of normal approximation
- Fluctuations of eigenvalues and second order Poincaré inequalities
- Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
- Two moments suffice for Poisson approximations: The Chen-Stein method
- Edgeworth expansions in very-high-dimensional problems
- Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces
- Gaussian approximation for high dimensional time series
- Gaussian approximation for high dimensional vector under physical dependence
- Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications
- The CLT in high dimensions: quantitative bounds via martingale embedding
- Entropy and the fourth moment phenomenon
- Explicit rates of convergence in the multivariate CLT for nonlinear statistics
- Approximating high-dimensional infinite-order \(U\)-statistics: statistical and computational guarantees
- Randomized incomplete \(U\)-statistics in high dimensions
- Existence of Stein kernels under a spectral gap, and discrepancy bounds
- A multivariate Berry-Esseen theorem with explicit constants
- Stein kernels and moment maps
- Stein's method, logarithmic Sobolev and transport inequalities
- Comparison and anti-concentration bounds for maxima of Gaussian random vectors
- Central limit theorems and bootstrap in high dimensions
- A high-dimensional CLT in \(\mathcal {W}_2\) distance with near optimal convergence rate
- Gaussian approximation of maxima of Wiener functionals and its application to high-frequency data
- Explicit rates of approximation in the CLT for quadratic forms
- Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
- Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
- Some Approximation Problems in Statistics and Probability
- Normal Approximations with Malliavin Calculus
- Inference on Causal and Structural Parameters using Many Moment Inequalities
- Higher-order Stein kernels for Gaussian approximation
- KOLMOGOROV DISTANCE FOR MULTIVARIATE NORMAL APPROXIMATION
- A Lyapunov-type Bound in Rd
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