Sub-Gaussian mean estimators

By Luc Devroye, Matthieu Lerasle, Gábor Lugosi, Roberto Imbuzeiro Oliveira. 2015

222 citations recorded by the source corpus.

We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic 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.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f700bbc2a3fb25e14edcf6d76abde2633e8e9aae

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In Artificial Intelligence

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Convergence rates of least squares regression estimators with heavy-tailed errors (2017, methodology): “We refer the readers to, for example, [18, 38, 40] and references therein for this line of research.”
Bispectrum Inversion with Application to Multireference Alignment (2017, methodology): “, with outliers, it might be useful to consider the median or the median of means method, see for instance [61].”
Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries (2016, methodology): “[DLLO15], this is sufficient to construct (via Lepski’s method [Lep92]) estimators that admit sub-Gaussian tails uniformly over t in a certain range.”
Distributed Statistical Estimation and Rates of Convergence in Normal Approximation (2017, background): “…acknowledge the works by Mcdonald et al. (2009); Zhang, Wainwright and Duchi (2012); Fan, Han and Liu (2014); Shafieezadeh-Abadeh, Esfahani and Kuhn (2015); Battey et al. (2015); Duchi et al. (2014); Lee et al. (2015); Cheng and Shang (2015); Rosenblatt and Nadler (2016); Zinkevich et al. (2010).”
Robust machine learning by median-of-means: Theory and practice (2017, background): “…where median-of-means estimators [2, 43, 73] provide a computationally tractable estimator satisfying optimal subgaussian concentration bounds [25], the other estimators are either suboptimal see for example [71] for the estimation of the mean of a vector in R d or [18] for more general…”
Mean Estimation and Regression Under Heavy-Tailed Distributions: A Survey (2019, unknown): “For more general versions we refer to [22].”
Adaptive Huber Regression (2017, methodology): “Further, Devroye et al. (2016) developed adaptive sub-Gaussian estimators that are independent of the prespecified exception probability.”