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Moment inequalities for U-statistics. (English) Zbl 1123.60009

The paper presents moment inequalities for completely degenerate, Banach space valued 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. The results generalize those of [E. Giné, R. Latala and J. Zinn, High dimensional probability II. 2nd international conference, Univ. of Washington, DC, USA, August 1–6, 1999. Boston, MA: Birkhäuser. Prog. Probab. 47, 13–38 (2000; Zbl 0969.60024)]. In the real valued case the results are used to obtain sharp estimates for moments and tails of canonical U-statistics . They are also used to obtain tail inequalities for multiple stochastic integrals of bounded deterministic functions with respect to stochastic processes with independent increments and uniformly bounded jumps.

MSC:

60E15 Inequalities; stochastic orderings

Citations:

Zbl 0969.60024

References:

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