Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exponential inequality for $U$-statistics of i.i.d. data   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 $h\left(X_1,\dots,X_r\right)$.
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
H\"older spaces is also considered.

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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn