Minimax Distribution Estimation in Wasserstein Distance

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.