Limit laws of the empirical Wasserstein distance: Gaussian distributions

作者：Rippl Thomas^*; Munk Axel; Sturm Anja

来源：Journal of Multivariate Analysis, 2016, 151: 90-109.

DOI：10.1016/j.jmva.2016.06.005

• Mallow's metric
• Transport metric
• Delta method
• Limit theorem
• Goodness-of-fit
• Frechet derivative
• Resolvent operator
• Bootstrap
• Elliptically symmetric distribution

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.

• 出版日期2016-10