Moment inequalities for U-statistics

Details Moment inequalities for U-statistics Moment inequalities for U-statistics

2005-06-01

arxiv.org/abs/math/0506026v2

Annals of Probability 2006, Vol. 34, No. 6, 2288-2314

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000476 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000476

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.

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