منابع مشابه
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...
متن کاملRobust 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 کاملU-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...
متن کاملU-Statistics Based on Spacings
In this paper, we investigate the asymptotic theory for U -statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U -statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit th...
متن کاملU-statistics Notes for Statistics 200c, Spring 2005
1. Definitions. The basic theory of U-statistics was developed by W. Hoeffding (1948a). Detailed expositions of the general topic may be found in M. Denker (1985) and A. J. Lee (1990). See also Fraser (1957) Chapter 6, Serfling (1980) Chapter 5, and Lehmann (1999) Chapter 6. Let P be a family of probability measures on an arbitrary measurable space. The problems treated here are nonparametric, ...
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ژورنال
عنوان ژورنال: Science
سال: 1965
ISSN: 0036-8075,1095-9203
DOI: 10.1126/science.147.3660.951