The Annals of Statistics

Sub-Gaussian mean estimators

Luc Devroye, Matthieu Lerasle, Gabor Lugosi, and Roberto I. Oliveira

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Abstract

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a nonasymptotic point of view. In particular, we define estimators with a sub-Gaussian behavior even for certain heavy-tailed distributions. We also prove various impossibility results for mean estimators.

Article information

Source
Ann. Statist., Volume 44, Number 6 (2016), 2695-2725.

Dates
Received: September 2015
Revised: January 2016
First available in Project Euclid: 23 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1479891632

Digital Object Identifier
doi:10.1214/16-AOS1440

Mathematical Reviews number (MathSciNet)
MR3576558

Zentralblatt MATH identifier
1360.62115

Subjects
Primary: 62G05: Estimation
Secondary: 60F99: None of the above, but in this section

Keywords
Sub-Gaussian estimators minimax bounds

Citation

Devroye, Luc; Lerasle, Matthieu; Lugosi, Gabor; Oliveira, Roberto I. Sub-Gaussian mean estimators. Ann. Statist. 44 (2016), no. 6, 2695--2725. doi:10.1214/16-AOS1440. https://projecteuclid.org/euclid.aos/1479891632


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