STATISTICAL INFERENCE FOR BURES-WASSERSTEIN BARYCENTERS

• 成果类型: Article
• 署名作者: Kroshnin, Alexey; Spokoiny, Vladimir; Suvorikova, Alexandra
• 署名单位: Russian Academy of Sciences; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1618
• 发表日期: 2021
• 页码: 1264-1298
• 关键词: CENTRAL-LIMIT-THEOREM; distance; matrix

摘要

In this work we introduce the concept of Bures-Wasserstein barycenter Q(*), that is essentially a Frechet mean of some distribution P supported on a subspace of positive semi-definite d-dimensional Hermitian operators H+(d). We allow a barycenter to be constrained to some affine subspace of H+(d), and we provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of Q(*) in both Frobenius norm and Bures-Wasserstein distance, and explain, how the obtained results are connected to optimal transportation theory and can be applied to statistical inference in quantum mechanics.