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2021 Robust and efficient mean estimation: an approach based on the properties of self-normalized sums
Stanislav Minsker, Mohamed Ndaoud
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Electron. J. Statist. 15(2): 6036-6070 (2021). DOI: 10.1214/21-EJS1925

Abstract

Let X be a random variable with unknown mean and finite variance. We present a new estimator of the mean of X that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation guarantees without any additional assumptions on the shape or tails of the distribution, and moreover is asymptotically efficient. This is the first estimator that provably combines all these qualities in one package. Our construction is inspired by robustness properties possessed by the self-normalized sums. Theoretical findings are supplemented by numerical simulations highlighting strong performance of the proposed estimator in comparison with previously known techniques.

Funding Statement

Authors acknowledge support by the National Science Foundation grants DMS-1712956 and CIF-1908905. M.N. was partially supported by a James H. Zumberge Faculty Research and Innovation Fund at the University of Southern California.

Citation

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Stanislav Minsker. Mohamed Ndaoud. "Robust and efficient mean estimation: an approach based on the properties of self-normalized sums." Electron. J. Statist. 15 (2) 6036 - 6070, 2021. https://doi.org/10.1214/21-EJS1925

Information

Received: 1 October 2020; Published: 2021
First available in Project Euclid: 27 December 2021

Digital Object Identifier: 10.1214/21-EJS1925

Keywords: efficiency , robust estimation , self-normalized sums , sub-Gaussian deviations

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Vol.15 • No. 2 • 2021
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