تقرير
On deviation probabilities in non-parametric regression
| العنوان: | On deviation probabilities in non-parametric regression |
|---|---|
| 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 |
| الوصف غير متاح. |