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Moment inequalities for U-statistics

Radosław Adamczak
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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.

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Radosław Adamczak. 2007-02-28. Moment inequalities for U-statistics. https://doi.org/10.1214/009117906000000476

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