Construction of Non-asymptotic Confidence Sets in 2 -Wasserstein Space - Johannes Ebert; Vladimir Spokoiny; Alexandra Suvorikova (Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series", 2018)
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.
Keywords: C00; 330; Wasserstein barycenters; hypothesis testing; multiplier bootstrap; change point detection; confidence sets