تقرير
Strong limit theorems for empirical halfspace depth trimmed regions
| العنوان: | Strong limit theorems for empirical halfspace depth trimmed regions |
|---|---|
| المؤلفون: | Ilienko, Andrii, Molchanov, Ilya, Turin, Riccardo |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Metric Geometry, Mathematics - Statistics Theory, 60F15 52A21 60D05 62H12 |
| الوصف: | We study empirical variants of the halfspace (Tukey) depth of a probability measure $\mu$, which are obtained by replacing $\mu$ with the corresponding weighted empirical measure. We prove analogues of the Marcinkiewicz--Zygmund strong law of large numbers and of the law of the iterated logarithm in terms of set inclusions and for the Hausdorff distance between the theoretical and empirical variants of depth trimmed regions. In the special case of $\mu$ being the uniform distribution on a convex body $K$, the depth trimmed regions are convex floating bodies of $K$, and we obtain strong limit theorems for their empirical estimators. Comment: 25 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.11393 |
| رقم الأكسشن: | edsarx.2308.11393 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |