On deviation probabilities in non-parametric regression
arxiv(2023)
摘要
This paper is devoted to the problem of determining the concentration bounds
that are achievable in non-parametric regression. We consider the setting where
features are supported on a bounded subset of ℝ^d, the regression
function is Lipschitz, and the noise is only assumed to have a finite second
moment. We first specify the fundamental limits of the problem by establishing
a general lower bound on deviation probabilities, and then construct explicit
estimators that achieve this bound. These estimators are obtained by applying
the median-of-means principle to classical local averaging rules in
non-parametric regression, including nearest neighbors and kernel procedures.
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