Аннотация:
The study of the asymptotic behavior of Ustatistics 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 Ustatistics 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 Ustatistics 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 Ustatistics whose data is a function of
i.i.d. random variables.
