Limit laws of the empirical Wasserstein distance: Gaussian distributions

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• 作者：Thomas Rippl^a ; ^{trippl@uni-goettingen.de" class="auth_mail" title="E-mail the corresponding author} ; Axel Munk^a ; ^b ; ^{munk@math.uni-goettingen.de" class="auth_mail" title="E-mail the corresponding author} ; Anja Sturm^a ; ^{asturm@math.uni-goettingen.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 62E20 ; 60F05 ; secondary ; 58C20 ; 90B06
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：151
• 期：Complete
• 页码：90-109
• 全文大小：560 K

文摘

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.