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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

144 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	2695-2725
Nombre de pages	31
journal	Annals of Statistics
Volume	44
Numéro de publication	6
Les DOIs	https://doi.org/10.1214/16-AOS1440
état	Publié - 1 déc. 2016
Modification externe	Oui

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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",

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AU - Lerasle, Matthieu

AU - Lugosi, Gabor

AU - Oliveira, Roberto I.

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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

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JO - Annals of Statistics

JF - Annals of Statistics

IS - 6

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Sub-Gaussian mean estimators

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