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Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions. J MULTIVARIATE ANAL 2019. [DOI: 10.1016/j.jmva.2018.09.014] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Bigot J, Klein T. Characterization of barycenters in the Wasserstein space by averaging optimal transport maps. ESAIM-PROBAB STAT 2018. [DOI: 10.1051/ps/2017020] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space. Using a duality argument, we give a precise characterization of the population barycenter for various parametric classes of random probability measures with compact support. In particular, we make a connection between averaging in the Wasserstein space as introduced in Agueh and Carlier [SIAM J. Math. Anal. 43 (2011) 904–924], and taking the expectation of optimal transport maps with respect to a fixed reference measure. We also discuss the usefulness of this approach in statistics for the analysis of deformable models in signal and image processing. In this setting, the problem of estimating a population barycenter from n independent and identically distributed random probability measures is also considered.
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Sommerfeld M, Munk A. Inference for empirical Wasserstein distances on finite spaces. J R Stat Soc Series B Stat Methodol 2017. [DOI: 10.1111/rssb.12236] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
| | - Axel Munk
- University of Göttingen; Germany
- Max Planck Institute for Biophysical Chemistry; Göttingen Germany
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