{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/multiplier-bootstrap-for-bures-wasserstein","title":"Generalized bootstrap in the Bures-Wasserstein space","arxiv_id":"2111.12612","date":"2021-11-24","proceeding":null,"authors":["Alexey Kroshnin","Vladimir Spokoiny","Alexandra Suvorikova"],"abstract":"This study proposes a bootstrap-based method for uncertainty quantification in two important statistical scenarios. First, we approximate the sampling distribution of empirical barycenters under the Bures--Wasserstein metric using a reweighted estimator. Our theoretical results guarantee the accuracy of this approximation and enable the construction of data-driven confidence sets. The methodology is validated through experiments on graph-structured data, including stochastic block models and brain connectomes. Additionally, we compare bootstrap-based confidence sets with the asymptotic confidence sets obtained in arXiv:1901.00226v2, evaluating both their statistical performance and computational complexity. Second, we investigate the generalized bootstrap framework for $M$-estimators without requiring a specific resampling scheme, thus covering both weighted and resampling methods under mild conditions. Both contributions rely on a novel Gaussian approximation result for $M$-estimators.","url_abs":"https://arxiv.org/abs/2111.12612v2","url_pdf":"https://arxiv.org/pdf/2111.12612v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"multiplier-bootstrap-for-bures-wasserstein","repo_url":"https://github.com/asuvor/bw_paper","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}