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Limit laws of the empirical Wasserstein distance: Gaussian distributions. (English) Zbl 1351.62064

Summary: 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.

MSC:

62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
90B06 Transportation, logistics and supply chain management
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