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December 2016 Sub-Gaussian mean estimators
Luc Devroye, Matthieu Lerasle, Gabor Lugosi, Roberto I. Oliveira
Ann. Statist. 44(6): 2695-2725 (December 2016). DOI: 10.1214/16-AOS1440

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.

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Luc Devroye. Matthieu Lerasle. Gabor Lugosi. Roberto I. Oliveira. "Sub-Gaussian mean estimators." Ann. Statist. 44 (6) 2695 - 2725, December 2016. https://doi.org/10.1214/16-AOS1440

Information

Received: 1 September 2015; Revised: 1 January 2016; Published: December 2016
First available in Project Euclid: 23 November 2016

zbMATH: 1360.62115
MathSciNet: MR3576558
Digital Object Identifier: 10.1214/16-AOS1440

Subjects:
Primary: 62G05
Secondary: 60F99

Keywords: minimax bounds , Sub-Gaussian estimators

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 6 • December 2016
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