Generalized bootstrap in the Bures--Wasserstein space
Authors
- Kroshnin, Alexey
- Spokoiny, Vladimir
ORCID: 0000-0002-2040-3427 - Suvorikova, Alexandra
ORCID: 0000-0001-9115-7449
2020 Mathematics Subject Classification
- 62F40
Keywords
- Bures-Wasserstein barycenter, bootstrap, generalized bootstrap, multiplier bootstrap
DOI
Abstract
This study focuses on finite-sample inference on the non-linear Bures-Wasserstein manifold and introduces a generalized bootstrap procedure for estimating Bures-Wasserstein barycenters. We provide non-asymptotic statistical guarantees for the resulting bootstrap confidence sets. The proposed approach incorporates classical resampling methods, including the multiplier bootstrap highlighted as a specific example. Additionally, the paper compares bootstrap-based confidence sets with asymptotic confidence sets obtained in the work of Kroshnin et al. [2021], evaluating their statistical performance and computational complexities. The methodology is validated through experiments on synthetic datasets and real-world applications.
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