منابع مشابه
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...
متن کاملOn the Estimation of Multiple Random Integrals and U-statistics
Fix a positive integer n, consider n independent and identically distributed random variables ξ1, . . . , ξn on a measurable space (X,X ) with some distribution μ and take their empirical distribution μn together with its normalization √ n(μn−μ). Beside this, take a function f(x1, . . . , xk) of k variables on the k-fold product (X k,X ) of the space (X,X ), introduce the k-th power of the norm...
متن کاملSequential Point Estimation of Estimable Parameters Based on U - Statistics
Asymptotically risk-efficient sequential point estimation of regular functionals of distribution functions based on U-statistics is considered under appropriate regularity conditions. Some auxiliary results on U-statistics are also considered in this context. fu~S Subject Classification: 62L12, 62LlS, 62G99.
متن کاملExtending Gossip Algorithms to Distributed Estimation of U-statistics
Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of U statistics, relying on more expensive averaging over pairs of observations, is a less investigated area. Yet, such data functionals are essential to describe...
متن کاملEstimation of Multiple Random Integrals and U-statistics
Here I give a short survey of some problems on multiple random integrals and U -statistics together with some other questions which occur during their study in a natural way. I write down the main results, discuss their background together with some pictures and mathematical ideas which explain them better. 2000 Math. Subj. Class. 60E15.
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2016
ISSN: 0304-4149
DOI: 10.1016/j.spa.2016.04.021