Limit laws of the empirical Wasserstein distance: Gaussian distributions

Understand

We derive central limit theorems for the Wasserstein distance between the empirical distributions of Gaussian samples.

• The cases are distinguished whether the underlying laws are the same or different.
• Results are based on the (quadratic) Frechet differentiability of the Wasserstein distance in the Gaussian case.
• Extensions to elliptically symmetric distributions are discussed as well as several applications such as bootstrap and statistical testing.