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arXiv · 1507.04090

Limit laws of the empirical Wasserstein distance: Gaussian distributions

Thomas Rippl·Axel Munk·Anja Sturm
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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) 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.

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Thomas Rippl, Axel Munk, Anja Sturm. 2015-07-15. Limit laws of the empirical Wasserstein distance: Gaussian distributions. https://arxiv.org/abs/1507.04090

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