Optimal bounds in non-Gaussian limit theorems for \(U\)-statistics

DOI10.1214/aop/1022677269zbMath1008.62017OpenAlexW2052239055MaRDI QIDQ1807184

Vidmantas Bentkus, Friedrich Götze

Publication date: 9 November 1999

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022677269

zbMATH Keywords

convergence ratescentral limit theoremEdgeworth expansionsU-statisticsBerry-Esseen boundssymmetric statisticsvon Mises statisticssecond order efficiencydegenerate U-statistics

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05)

Related Items (10)

On bounds for some U-statistics under the two-eigenvalues assumption ⋮ On distribution of error of linear wavelet estimator of probability density ⋮ Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space ⋮ Edgeworth approximations for distributions of symmetric statistics ⋮ Computational aspects of Cui-Freeden statistics for equidistribution on the sphere ⋮ Asymptotic analysis of symmetric functions ⋮ Statistical properties of $b$-adic diaphonies ⋮ Asymptotic Expansions for the Distributions of Canonical $V$-Statistics of Third Order ⋮ Asymptotic expansions in non-central limit theorems for quadratic forms ⋮ Nonlinear stochastic programming by Monte-Carlo estimators

Cites Work

• Unnamed Item
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• Asymptotic expansions for distributions of sums of independent random elements of a Hilbert space
• A refinement of the error estimate of the normal approximation in a Hilbert space
• Multiple Wiener-Ito integrals. With applications to limit theorems
• Convex measures on locally convex spaces
• Asymptotic expansions in the integral and local limit theorems in Banach spaces with applications to \(\omega\)-statistics
• On the lattice point problem for ellipsoids
• Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces
• Bounds for the accuracy of Poissonian approximations of stable laws
• Sums and Gaussian vectors
• Optimal rates of convergence in the CLT for quadratic forms
• Multiple Wiener integral
• Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
• On the Accuracy of Normal Approximation of the Probability of Hitting a Ball
• Approximation of quadratic forms of independent random vectors by accompanying laws
• On the Rate of Convergence in the Central Limit Theorem in Certain Banach Spaces
• Asymptotic expansions for bivariate von Mises functionals
• A Regular Estimate of the Accuracy of Normal Approximation in Hilbert Space
• Asymptotic Approximations for the Probability that a Sum of Lattice Random Vectors Lies in a Convex Set
• Skorohod embedding of multivariate RV's, and the sample DF
• Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes

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