Limit laws of the empirical Wasserstein distance: Gaussian distributions

Thomas Rippl, Axel Munk and Anja Sturm

Journal of Multivariate Analysis, 2016, vol. 151, issue C, 90-109

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.

Keywords: Mallow’s metric; Transport metric; Delta method; Limit theorem; Goodness-of-fit; Fréchet derivative; Resolvent operator; Bootstrap; Elliptically symmetric distribution (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:151:y:2016:i:c:p:90-109

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DOI: 10.1016/j.jmva.2016.06.005

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