## The Annals of Probability

### Moment inequalities for U-statistics

#### Abstract

We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the real-valued case, can be replaced by simpler norms of the kernel matrix (i.e., norms of some multilinear operators associated with the kernel matrix). As a corollary, we derive tail inequalities for U-statistics with bounded kernels and for some multiple stochastic integrals.

#### Article information

Source
Ann. Probab. Volume 34, Number 6 (2006), 2288-2314.

Dates
First available in Project Euclid: 13 February 2007

https://projecteuclid.org/euclid.aop/1171377443

Digital Object Identifier
doi:10.1214/009117906000000476

Mathematical Reviews number (MathSciNet)
MR2294982

Zentralblatt MATH identifier
1123.60009

Subjects
Primary: 60E15: Inequalities; stochastic orderings

#### Citation

Adamczak, Radosław. Moment inequalities for U-statistics. Ann. Probab. 34 (2006), no. 6, 2288--2314. doi:10.1214/009117906000000476. https://projecteuclid.org/euclid.aop/1171377443

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