Title: Minimax Distribution Estimation in Wasserstein Distance,
Abstract: The Wasserstein metric is an important measure of distance between
probability distributions, with applications in machine learning, statistics,
probability theory, and data analysis. This paper provides upper and lower
bounds on statistical minimax rates for the problem of estimating a probability
distribution under Wasserstein loss, using only metric properties, such as
covering and packing numbers, of the sample space, and weak moment assumptions
on the probability distributions.