Robust non-parametric regression via median-of-means

01/25/2023

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by   Anna Ben-Hamou, et al.

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In this paper, we apply the median-of-means principle to derive robust versions of local averaging rules in non-parametric regression. For various estimates, including nearest neighbors and kernel procedures, we obtain non-asymptotic exponential inequalities, with only a second moment assumption on the noise. We then show that these bounds cannot be significantly improved by establishing a corresponding lower bound on tail probabilities.