Deviation and moment inequalities for Banach-valued $U$-statistics

Davide Giraudo (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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 Hölderian functional central limit theorem and a moment inequality for incomplete $U$-statistics.

Mots clés: U -statistics; martingales; Banach space.

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Davide Giraudo. Deviation and moment inequalities for Banach-valued $U$-statistics. 2024. ⟨hal-04566956⟩