Аннотация:
The study of the asymptotic behavior of U-statistics has
concentrated a lot of attention since the seminal work by Hoeffding
(1963), due to its applications in particular to statistics and random
geometry. In this talk, we will review some results on U-statistics of
i.i.d. data (Hoeffding's decomposition, law of large numbers, law of the
iterated logarithms, central limit theorem) and give an exponential
inequality for U-statistics of i.i.d. data and furnish applications to
the rates in the strong law of large numbers and functional central
limit theorems in Hölder spaces. Then we will deal with a generalized
Hoeffding's decomposition for U-statistics whose data is a function of
i.i.d. random variables.
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