On deviation probabilities in non-parametric regression with heavy-tailed noise
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909406703124480 |
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| author | Ben-Hamou, Anna Guyader, Arnaud |
| author_facet | Ben-Hamou, Anna Guyader, Arnaud |
| contents | 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 $\mathbb{R}^d$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10498 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On deviation probabilities in non-parametric regression with heavy-tailed noise Ben-Hamou, Anna Guyader, Arnaud Statistics Theory 62G08, 62G15, 62G35 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 $\mathbb{R}^d$, 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. |
| title | On deviation probabilities in non-parametric regression with heavy-tailed noise |
| topic | Statistics Theory 62G08, 62G15, 62G35 |
| url | https://arxiv.org/abs/2301.10498 |