The Annals of Statistics

On local U-statistic processes and the estimation of densities of functions of several sample variables

Evarist Giné and David M. Mason

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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) 517–525] and, as a consequence, uniform in bandwidth central limit theorems in the sup and in the Lp norms are obtained for these estimators.

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Ann. Statist., Volume 35, Number 3 (2007), 1105-1145.

First available in Project Euclid: 24 July 2007

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60F15: Strong theorems 62E20: Asymptotic distribution theory 62G30: Order statistics; empirical distribution functions

U-statistics central limit theorems empirical process kernel density estimation


Giné, Evarist; Mason, David M. On local U -statistic processes and the estimation of densities of functions of several sample variables. Ann. Statist. 35 (2007), no. 3, 1105--1145. doi:10.1214/009053607000000154.

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