تقرير
On deviation probabilities in non-parametric regression
العنوان: | On deviation probabilities in non-parametric regression |
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المؤلفون: | Ben-Hamou, Anna, Guyader, Arnaud |
سنة النشر: | 2023 |
المجموعة: | Mathematics Statistics |
مصطلحات موضوعية: | Mathematics - Statistics Theory, 62G08, 62G15, 62G35 |
الوصف: | 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. Comment: The lower bound has been improved and the paper has been reorganized |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2301.10498 |
رقم الأكسشن: | edsarx.2301.10498 |
قاعدة البيانات: | arXiv |
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