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  Limit laws of the empirical Wasserstein distance: Gaussian distributions.

Rippl, T., Munk, A., & Sturm, A. (2016). Limit laws of the empirical Wasserstein distance: Gaussian distributions. Journal of Multivariate Analysis, 151, 90-109. doi:10.1016/j.jmva.2016.06.005.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-9A7C-E Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-9A7F-8
Genre: Journal Article

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2351923.pdf (Publisher version), 561KB
 
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 Creators:
Rippl, T., Author
Munk, A.1, Author              
Sturm, A., Author
Affiliations:
1Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society, ou_1113580              

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Free keywords: Mallow's metric; Transport metric; Delta method; Limit theorem; Goodness-of-fit; Frechet derivative; Resolvent operator; Bootstrap; Elliptically symmetric distribution
 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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Language(s): eng - English
 Dates: 2016-07-192016-10
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1016/j.jmva.2016.06.005
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Title: Journal of Multivariate Analysis
Source Genre: Journal
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Pages: - Volume / Issue: 151 Sequence Number: - Start / End Page: 90 - 109 Identifier: -