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.
Citation
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
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