Moment inequalities for Ustatistics
Abstract
We present moment inequalities for completely degenerate Banach space valued (generalized) Ustatistics of arbitrary order. The estimates involve suprema of empirical processes which, in the realvalued 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 Ustatistics with bounded kernels and for some multiple stochastic integrals.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2005
 DOI:
 10.48550/arXiv.math/0506026
 arXiv:
 arXiv:math/0506026
 Bibcode:
 2005math......6026A
 Keywords:

 Mathematics  Probability;
 60E15 (Primary)
 EPrint:
 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)