Deviation and moment inequalities for Banach-valued $U$-statistics
Probability
2024-05-06 v1 Statistics Theory
Statistics Theory
Abstract
We show a deviation inequality for U-statistics of independent data taking values in a separable Banach space which satisfies some smoothness assumptions. We then provide applications to rates in the law of large numbers for U-statistics, a H{\"o}lderian functional central limit theorem and a moment inequality for incomplete -statistics.
Keywords
Cite
@article{arxiv.2405.01902,
title = {Deviation and moment inequalities for Banach-valued $U$-statistics},
author = {Davide Giraudo},
journal= {arXiv preprint arXiv:2405.01902},
year = {2024}
}