Fetching the paper…

Reading the bibliography…

2015

Sub-Gaussian mean estimators

Devroye, Luc, Lerasle, Matthieu, Lugosi, Gabor et al.

Original
PDF
Post on X

Understand

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.

Sub-Gaussian mean estimators · Around

Built on

Sums of Independent Random Variables
V.V. Petrov · 1975
Earlier work this paper cites.
Problem Complexity and Method Efficiency in Optimization
A. Nemirovsky and D. Yudin · 1983
Earlier work this paper cites.
Random generation of combinatorial structures from a uniform distribution
M. Jerrum, L. Valiant, and V. Vazirani · 1986
Earlier work this paper cites.
On a problem of adaptive estimation in Gaussian white noise
O. V. Lepskii · 1990
Earlier work this paper cites.
Asymptotically minimax adaptive estimation I: Upper bounds. optimally adaptive estimates
O. V. Lepskii · 1991
Earlier work this paper cites.
The space complexity of approximating the frequency moments
N. Alon, Y. Matias, and M. Szegedy · 1996
Earlier work this paper cites.

Similar

Probability theory: an analytic view
D. W. Stroock · 2003
Cited alongside, same era.
Notes for miscellaneous lectures
L. A. Levin · 2005
Cited alongside, same era.
Robust statistics
D. Hsu · 2010
Cited alongside, same era.
Robust linear least squares regression
J.-Y. Audibert and O. Catoni · 2011
Cited alongside, same era.
Challenging the empirical mean and empirical variance: A deviation study
O. Catoni · 2012
Cited alongside, same era.

Then

Robust empirical mean estimators
Original
M. Lerasle and R. I. Oliveira · 2012
Later among the works it cites.
Bandits with heavy tail
S. Bubeck, N. Cesa-Bianchi, and G. Lugosi · 2013
Later among the works it cites.
Geometric median and robust estimation in Banach spaces
S. Minsker · 2013
Later among the works it cites.
Heavy-tailed regression with a generalized median-of-means
D. Hsu and S. Sabato · 2014
Later among the works it cites.
Empirical risk minimization for heavy-tailed losses
C. Brownlees, E. Joly, and G. Lugosi · 2015
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…