Limit laws of the empirical Wasserstein distance: Gaussian distributions
2016 | journal article; research paper. A publication with affiliation to the University of Göttingen.
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- Authors
- Rippl, Thomas; Munk, Axel ; Sturm, Anja
- Abstract
- 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) Fréchet 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.
- Issue Date
- 2016
- Journal
- Journal of Multivariate Analysis
- ISSN
- 0047-259X
- Language
- English