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Robust empirical mean Estimators
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abstract
We study robust estimators of the mean of a probability measure $P$, called robust empirical mean estimators. This elementary construction is then used to revisit a problem of aggregation and a problem of estimator selection, extending these methods to not necessarily bounded collections of previous estimators. We consider then the problem of robust $M$-estimation. We propose a slightly more complicated construction to handle this problem and, as examples of applications, we apply our general approach to least-squares density estimation, to density estimation with K\"ullback loss and to a non-Gaussian, unbounded, random design and heteroscedastic regression problem. Finally, we show that our strategy can be used when the data are only assumed to be mixing.
Forward citations
Cited by 2 Pith papers
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Improved Concentration for Mean Estimators via Shrinkage
A general class of shrinkage-based robust mean estimators is shown to attain near-optimal sub-Gaussian concentration whenever the base estimator has bounded error and is computed on an independent sample.
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On the Benefits of Accelerated Optimization in Robust and Private Estimation
Momentum-accelerated Frank-Wolfe and gradient descent reduce both iteration counts and privacy noise for private and heavy-tailed-robust estimation, yielding rates such as 1/(nε) instead of 1/(nε)^{2/3}.
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