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 $U$-statistics.

翻译：我们证明了在满足某些光滑性假设的可分Banach空间中，对于独立数据取值的U统计量存在偏差不等式。随后，我们将其应用于U统计量的大数定律收敛速率、基于Hölder泛函中心极限定理以及不完全$U$统计量的矩不等式。