WIAS Preprint No. 3145, (2024)

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

10.20347/WIAS.PREPRINT.3145

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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