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November 2006 Moment inequalities for U-statistics
Radosław Adamczak
Ann. Probab. 34(6): 2288-2314 (November 2006). DOI: 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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Radosław Adamczak. "Moment inequalities for U-statistics." Ann. Probab. 34 (6) 2288 - 2314, November 2006.


Published: November 2006
First available in Project Euclid: 13 February 2007

zbMATH: 1123.60009
MathSciNet: MR2294982
Digital Object Identifier: 10.1214/009117906000000476

Primary: 60E15

Keywords: concentration of measure , U-statistics

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 6 • November 2006
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