SUB-GAUSSIAN MEAN ESTIMATORS

• 成果类型: Article
• 署名作者: Devroye, Luc; Lerasle, Matthieu; Lugosi, Gabor; Olivetra, Roberto I.
• 署名单位: McGill University; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Pompeu Fabra University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1440
• 发表日期: 2016
• 页码: 2695-2725
• 关键词: Adaptive Estimation

摘要

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.