Uniform bounds for robust mean estimators

Stanislav Minsker

Stochastic Processes and their Applications, 2025, vol. 190, issue C

Abstract: We study estimators of the means of a family of random variables {f(X),f∈F} that admit uniform, over the class F of real-valued functions, non-asymptotic error bounds under minimal moment assumptions on the underlying distribution. We show that known robust methods, such as the median-of-means and Catoni’s estimators, can often be viewed as special cases of our construction. The paper’s primary contribution lies in establishing uniform bounds for the deviations of stochastic processes defined by the proposed estimators. Furthermore, we analyze the stability of these estimators within the context of the ‘adversarial contamination’ framework. Finally, we demonstrate the applicability of our methods to the problem of robust multivariate mean estimation, showing that the resulting inequalities achieve optimal dependence on the parameters of the problem.

Keywords: Robust estimation; Median of means; Concentration of measure; Adversarial contamination (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414925001656
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:190:y:2025:i:c:s0304414925001656

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2025.104724

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().