Generalized bootstrap in the Bures-Wasserstein space

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 sets obtained in the work arXiv:1901.00226v2, evaluating their statistical performance and computational complexities. The methodology is validated through experiments on synthetic datasets and real-world applications.