Moment inequalities for U-statistics

Adamczak, Radosław

Ann. Probab., Tome 34 (2006) no. 1, p. 2288-2314 / Harvested from Project Euclid

Résumé

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.

Publié le : 2006-11-14
Classification: U-statistics, concentration of measure, 60E15

@article{1171377443,
     author = {Adamczak, Rados\l aw},
     title = {Moment inequalities for U-statistics},
     journal = {Ann. Probab.},
     volume = {34},
     number = {1},
     year = {2006},
     pages = { 2288-2314},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1171377443}
}

Adamczak, Radosław. Moment inequalities for U-statistics. Ann. Probab., Tome 34 (2006) no. 1, pp.  2288-2314. http://gdmltest.u-ga.fr/item/1171377443/