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2020 Exact rate of convergence of the expected $W_{2}$ distance between the empirical and true Gaussian distribution
Philippe Berthet, Jean Claude Fort
Electron. J. Probab. 25: 1-16 (2020). DOI: 10.1214/19-EJP410

Abstract

We study the Wasserstein distance $W_{2}$ for Gaussian samples. We establish the exact rate of convergence $\sqrt{\log \log n/n} $ of the expected value of the $W_{2}$ distance between the empirical and true $c.d.f.$’s for the normal distribution. We also show that the rate of weak convergence is unexpectedly $1/\sqrt{n} $ in the case of two correlated Gaussian samples.

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Philippe Berthet. Jean Claude Fort. "Exact rate of convergence of the expected $W_{2}$ distance between the empirical and true Gaussian distribution." Electron. J. Probab. 25 1 - 16, 2020. https://doi.org/10.1214/19-EJP410

Information

Received: 5 June 2019; Accepted: 25 December 2019; Published: 2020
First available in Project Euclid: 29 January 2020

zbMATH: 1440.62157
MathSciNet: MR4059190
Digital Object Identifier: 10.1214/19-EJP410

Subjects:
Primary: 60F05, 60F17, 62G20, 62G30

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