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キーワード:
Mallow's metric; Transport metric; Delta method; Limit theorem; Goodness-of-fit; Frechet derivative; Resolvent operator; Bootstrap; Elliptically symmetric distribution
要旨:
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.
