Sub-Gaussian mean estimators

Luc Devroye; Matthieu Lerasle; Gabor Lugosi; Roberto I. Oliveira

doi:10.1214/16-AOS1440

Sub-Gaussian mean estimators

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

McGill University
Université de Nice
Universitat Pompeu Fabra
IMPA

Research output: Contribution to journal › Article › peer-review

143 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2695-2725
Number of pages	31
Journal	Annals of Statistics
Volume	44
Issue number	6
DOIs	https://doi.org/10.1214/16-AOS1440
Publication status	Published - 1 Dec 2016
Externally published	Yes

Keywords

Minimax bounds
Sub-Gaussian estimators

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10.1214/16-AOS1440

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title = "Sub-Gaussian mean estimators",

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.",

keywords = "Minimax bounds, Sub-Gaussian estimators",

author = "Luc Devroye and Matthieu Lerasle and Gabor Lugosi and Oliveira, \{Roberto I.\}",

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year = "2016",

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AU - Lugosi, Gabor

AU - Oliveira, Roberto I.

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N2 - 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.

AB - 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.

KW - Minimax bounds

KW - Sub-Gaussian estimators

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DO - 10.1214/16-AOS1440

M3 - Article

AN - SCOPUS:84999767783

SN - 0090-5364

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EP - 2725

JO - Annals of Statistics

JF - Annals of Statistics

IS - 6

ER -

Sub-Gaussian mean estimators

Abstract

Keywords

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