Limiting cumulants of U-statistics

Lecture 4: U-Statistics & U-Process Minimizers

Hoeffding (1948a) developed the basic theory of U-Statistics, a family of estimates which includes many familiar and interesting examples. This lecture reviews this theory. Standard references for the material presented here include Serfling (1980, Chapter 5), Lehmman (1999, Chapter 6) and van der Vaart (1998, Chapters 11 & 12). The basic theory of U-Statistics allows for a presentation of larg...

Robust estimation of U-statistics

An important part of the legacy of Evarist Giné is his fundamental contributions to our understanding of U -statistics and U -processes. In this paper we discuss the estimation of the mean of multivariate functions in case of possibly heavy-tailed distributions. In such situations, reliable estimates of the mean cannot be obtained by usual U -statistics. We introduce a new estimator, based on t...

Charge sensitive cumulants and flow in U+U collisions from STAR

Limiting Distribution of the G Statistics

The G statistic and its local version have been used extensively in spatial data analysis. The paper proves the asymptotic normality of the G statistic. Theorems in this paper imply the regular permutation test for the G statistic is valid.

U-statistics in stochastic geometry

A U-statistic of order k with kernel f :X →Rd over a Poisson process is defined in [25] as ∑ x1,...,xk∈η 6= f (x1, . . . ,xk) under appropriate integrability assumptions on f . U-statistics play an important role in stochastic geometry since many interesting functionals can be written as Ustatistics, like intrinsic volumes of intersection processes, characteristics of random geometric graphs, v...