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arXiv · 2610.15974

Robust Nonparametric Methods for $α$-Mixing Sequences via Median-of-Means

Attila Lovas·Marcell Tukora
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Abstract

The median-of-means (MoM) estimator is a robust alternative to the sample mean for heavy-tailed or contaminated data. While its non-asymptotic properties are well understood for i.i.d.\ samples, much less is known for dependent sequences. We establish non-asymptotic deviation bounds for the MoM estimator computed from consecutive blocks of an identically distributed $α$-mixing sequence, both for a single mean and uniformly over a class of functions (the median-of-means process). All bounds remain valid, with explicitly adjusted constants, when a sufficiently small fraction of the blocks is adversarially corrupted. As applications, we obtain deviation bounds for a median-of-means Nadaraya--Watson regression estimator, for the MoM kernel density estimator, and for empirical and Bahadur-type estimators of Value-at-Risk and Conditional Value-at-Risk. Finally, we show that the sampling of bulk materials, where the measurements form a spatially dependent random field, reduces to the one-dimensional setting if the samples are taken in well-separated groups.

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BibTeXRIS

Attila Lovas, Marcell Tukora. 2026-10-11. Robust Nonparametric Methods for $α$-Mixing Sequences via Median-of-Means. https://arxiv.org/abs/2610.15974

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