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