Abstract
Hoeffding introduced U-statistics in 1948, partly influenced by earlier work of Halmos, and closely connected to von Rises’ functionals (von Mises, 1947). U-statistics can be viewed as a class of unbiased estimators of a certain parameter, based on some averaging procedure.
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Notes on chapter 1
The decomposition method discussed in section 2 is due to Hoeffding (1948) as well as the asymptotic normality in section 3. In the generalized case this was done by Lehmann (1951). The backward martingale property goes back to Berk (1966) and the invariance principles have been stated by Miller and Sen (1972, 1974). The law of the iterated logarithm is due to Serfling. The book of Randies and Wolfe (1979) contains an extensive discussion of examples and applications and Serfling’s book (1980) contains further results on U- and V-statistics in the non-degenerate case.
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© 1985 Springer Fachmedien Wiesbaden
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Denker, M. (1985). U-statistics. In: Asymptotic Distribution Theory in Nonparametric Statistics. Advanced Lectures in Mathematics. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14229-4_1
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DOI: https://doi.org/10.1007/978-3-663-14229-4_1
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08905-4
Online ISBN: 978-3-663-14229-4
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