Sub-Gaussian estimators of the mean of a random vector

Gábor Lugosi; Shahar Mendelson

doi:10.1214/17-AOS1639

Sub-Gaussian estimators of the mean of a random vector

Gábor Lugosi, Shahar Mendelson

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

111 Citations (Scopus)

Abstract

We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median.

Original language	English
Pages (from-to)	783-794
Number of pages	12
Journal	Annals of Statistics
Volume	47
Issue number	2
DOIs	https://doi.org/10.1214/17-AOS1639
Publication status	Published - Apr 2019

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title = "Sub-Gaussian estimators of the mean of a random vector",

abstract = "We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median.",

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AB - We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median.

KW - Mean estimation

KW - Robust estimation

KW - Sub-Gaussian inequalities

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Sub-Gaussian estimators of the mean of a random vector

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