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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: IRTG 1792 Discussion Paper ; No. 2018-025

Klassifikation und Themen

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

Beteiligte, Orts- und Zeitangaben

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

Weitere Informationen

• Handle: http://hdl.handle.net/10419/230736
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ