An exponential inequality for U-statistics of i.i.d. data

2019/11/13 by Giraudo, Davide
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1911.05502

Abstract

We establish an exponential inequality for degenerated U-statistics of order r of i.i.d. data. This inequality gives a control of the tail of the maxima absolute values of the U-statistic by the sum of two terms: an exponential term and one involving the tail of h(X₁,…,X_r). We also give a version for not necessarily degenerated U-statistics having a symmetric kernel and furnish an application to the convergence rates in the Marcinkiewicz law of large numbers. Application to invariance principle in Hölder spaces is also considered.

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