The Annals of Statistics

Sub-Gaussian estimators of the mean of a random vector

Gábor Lugosi and Shahar Mendelson

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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.

Article information

Source
Ann. Statist., Volume 47, Number 2 (2019), 783-794.

Dates
Received: February 2017
Revised: July 2017
First available in Project Euclid: 11 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.aos/1547197238

Digital Object Identifier
doi:10.1214/17-AOS1639

Mathematical Reviews number (MathSciNet)
MR3909950

Zentralblatt MATH identifier
07033151

Subjects
Primary: 62J02: General nonlinear regression 62G08: Nonparametric regression
Secondary: 60G25: Prediction theory [See also 62M20]

Keywords
Mean estimation robust estimation sub-Gaussian inequalities

Citation

Lugosi, Gábor; Mendelson, Shahar. Sub-Gaussian estimators of the mean of a random vector. Ann. Statist. 47 (2019), no. 2, 783--794. doi:10.1214/17-AOS1639. https://projecteuclid.org/euclid.aos/1547197238


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