Title: U-Statistics in Banach Spaces
Description: U-statistics are universal objects of modern probabilistic summation theory. They appear in various statistical problems and have very important applications. The mathematical nature of this class of random variables has a functional character and, therefore, leads to the investigation of probabilistic distributions in infinite-dimensional spaces. The situation when the kernel of a U-statistic takes values in a Banach space, turns out to be the most natural and interesting.
Subjects: Estimation theory, Banach spaces, Central limit theorems, Random variables, Mathematical statistics, Order statistics, Stochastic processes, Asymptotic expansion, U-statistics, Law of large numbers