Exact rate of convergence of the expected \(W_2\) distance between the empirical and true Gaussian distribution

DOI10.1214/19-EJP410zbMath1440.62157arXiv2001.09817OpenAlexW3105132204MaRDI QIDQ2184570

Philippe Berthet, Jean-Claude Fort

Publication date: 29 May 2020

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

Full work available at URL: https://arxiv.org/abs/2001.09817

zbMATH Keywords

empirical processescentral limit theoremstrong approximationquadratic Wasserstein distanceGaussian empirical cumulative distribution function (c.d.f.)

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Functional limit theorems; invariance principles (60F17)

Related Items (6)

On the quadratic random matching problem in two-dimensional domains ⋮ A note on recovering the Brownian motion component from a Lévy process ⋮ Optimal Matching of Random Samples and Rates of Convergence of Empirical Measures ⋮ Implementable coupling of Lévy process and Brownian motion ⋮ Monitoring for a change point in a sequence of distributions ⋮ On optimal matching of Gaussian samples III

Cites Work

• Unnamed Item
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• Probability in Banach spaces. Isoperimetry and processes
• The Brunn-Minkowski inequality in Gauss space
• Asymptotic expansions for the power of distributionfree tests in the two- sample problem
• Asymptotics for \(L_2\) functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances
• A central limit theorem for Wasserstein type distances between two distinct univariate distributions
• Convergence of integrals of uniform empirical and quantile processes
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances

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