论文标题
经验分布和真实高斯之间平均瓦斯汀距离的精确收敛速率
Exact rate of convergence of the mean Wasserstein distance between the empirical and true Gaussian distribution
论文作者
论文摘要
我们研究Wasserstein距离$ W_2 $用于高斯样品。我们建立了收敛的确切速率$ \ sqrt {\ log \ log \ log n/n} $的预期价值的经验和真实$c.d.f。$之间的$ W_2 $距离。我们还表明，在两个相关的高斯样本的情况下，弱收敛的速率是$ 1/\ sqrt {n} $。
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.
