Multivariate mean estimation with direction-dependent accuracy

Mostra el registre complet Registre parcial de l'ítem

• dc.contributor.author Lugosi, Gábor
• dc.contributor.author Mendelson, Shahar
• dc.date.accessioned 2025-06-17T15:51:14Z
• dc.date.available 2025-06-17T15:51:14Z
• dc.date.issued 2024
• dc.date.updated 2025-06-17T15:51:14Z
• dc.description.abstract We consider the problem of estimating the mean of a random vector based on N independent, identically distributed observations.We prove the existence of an estimator that has a nearoptimal error in all directions in which the variance of the one-dimensional marginal of the random vector is not too small: with probability 1−δ, the procedure returns μN which satisfies, for every direction u∈Sd−1, ⟨μN−μ,u⟩≤NC(σ(u)log(1/δ)+(E∥X−EX∥2)1/2), where σ2(u)=Var(⟨X,u⟩) and C is a constant. To achieve this, we require only slightly more than the existence of the covariance matrix, in the form of a certain moment-equivalence assumption.
• dc.description.sponsorship Gábor Lugosi was supported by the Spanish Ministry of Economy and Competitivity, Grant PGC2018-101643-B-I00 and FEDER, EU, and by 'Google Focused Award Algorithms and Learning for AI'.
• dc.format.mimetype application/pdf
• dc.identifier.citation Lugosi G, Mendelson S. Multivariate mean estimation with direction-dependent accuracy. J. Eur. Math. Soc. 2024;26(6):2211-47. DOI: 10.4171/JEMS/1321
• dc.identifier.doi http://dx.doi.org/10.4171/JEMS/1321
• dc.identifier.issn 1435-9855
• dc.identifier.uri http://hdl.handle.net/10230/70707
• dc.language.iso eng
• dc.publisher European Mathematical Society (EMS)
• dc.relation.ispartof Journal of the European Mathematical Society. 2024;26(6):2211-47
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/PGC2018-101643-B-I00
• dc.rights © 2023 European Mathematical Society. Published by EMS Press and licensed under a CC BY 4.0 license.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Mean estimation
• dc.subject.keyword High-dimensional statistics
• dc.subject.keyword Robust statistics
• dc.title Multivariate mean estimation with direction-dependent accuracy
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion