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

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: IRTG 1792 Discussion Paper ; No. 2018-025

Classification and Topics

• Classification: Wirtschaft ; Mathematical and Quantitative Methods: General
• Subject: Wasserstein barycenters ; hypothesis testing ; multiplier bootstrap ; change point detection ; confidence sets

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Ebert, Johannes ; Spokoiny, Vladimir ; Suvorikova, Alexandra
• Event: Veröffentlichung
• (who): Humboldt-Universität zu Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"
• (where): Berlin
• (when): 2018

Further information

• Handle: http://hdl.handle.net/10419/230736
• Last update: 10.03.2025, 11:42 AM CET