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Ebert, Johannes
Spokoiny, Vladimir
Suvorikova, Alexandra
Year of Publication: 
Series/Report no.: 
IRTG 1792 Discussion Paper No. 2018-025
In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2 -Wasserstein space and develop the idea further to construction of a non-parametric two-sample test that is then applied to the detection of structural breaks in data with complex geometry. Both procedures mainly rely on the idea of multiplier bootstrap (Spokoiny and Zhilova [29], Chernozhukov, Chetverikov and Kato [13]). The main focus lies on probability measures that have commuting covariance matrices and belong to the same scatter-location family: we proof the validity of a bootstrap procedure that allows to compute confidence sets and critical values for a Wasserstein-based two-sample test.
Wasserstein barycenters
hypothesis testing
multiplier bootstrap
change point detection
confidence sets
Document Type: 
Working Paper

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