Construction of Non-asymptotic Confidence Sets in 2 -Wasserstein Space

Johannes Ebert, Vladimir Spokoiny and Alexandra Suvorikova

No 2018-025, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: 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: Wasserstein barycenters; hypothesis testing; multiplier bootstrap; change point detection; confidence sets (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:irtgdp:2018025

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