We obtain sharp upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from $n$ samples. A version of this result for probability measures on Banach spaces is also obtained.

翻译：我们在可分离希尔伯特空间上的概率测度与其基于$n$个样本的经验分布之间的期望最大切片1-Wasserstein距离上获得了精确的上界和下界。对于巴拿赫空间上的概率测度，我们同样得到了该结果的一个版本。