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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- June 2005
- DOI:
- 10.48550/arXiv.math/0506026
- arXiv:
- arXiv:math/0506026
- Bibcode:
- 2005math......6026A
- Keywords:
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- Mathematics - Probability;
- 60E15 (Primary)
- E-Print:
- Published at http://dx.doi.org/10.1214/009117906000000476 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)