A notion of local U -statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U -processes that may be useful in other contexts. This local U -statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer. Statist. Assoc. 89 (1994) 51...

A notion of local U -statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U -processes that may be useful in other contexts. This local U -statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer. Statist. Assoc. 89 (1994) 51...

We compare several simulation estimators for a performance measure of a process having multiple regeneration sequences. We examine the setting of two regeneration sequences. We compare two existing estimators, the permuted estimator and the semi-regenerative estimator, and two new estimators, a type of U -statistic estimator and a type of V -statistic estimator. The last two estimators are obta...

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...

Let X1, . . . ,Xn be i.i.d. random observations. Let S = L + T be a U -statistic of order k ≥ 2, where L is a linear statistic having asymptotic normal distribution, and T is a stochastically smaller statistic. We show that the rate of convergence to normality for S can be simply expressed as the rate of convergence to normality for the linear part L plus a correction term, (varT) ln(varT), und...

We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Therefore, several standard theorems on properties of U-statistics apply. In particular, it has minimal variance among all unbiased estimators and is asymptotically normal...