Exact rate of convergence of the mean Wasserstein distance between the empirical and true Gaussian distribution

01/27/2020

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by   Philippe Berthet, et al.

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We study the Wasserstein distance W_2 for Gaussian samples. We establish the exact rate of convergence √(loglog 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/√(n) in the case of two correlated Gaussian samples.