Exact rate of convergence of the expected $W_{2}$ distance between the empirical and true Gaussian distribution
Résumé
We study the Wasserstein distance W 2 for Gaussian samples. We establish the exact rate of convergence 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/ √ n in the case of two correlated Gaussian samples.
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