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July 2007 On local U-statistic processes and the estimation of densities of functions of several sample variables
Evarist Giné, David M. Mason
Ann. Statist. 35(3): 1105-1145 (July 2007). DOI: 10.1214/009053607000000154

Abstract

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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Evarist Giné. David M. Mason. "On local U-statistic processes and the estimation of densities of functions of several sample variables." Ann. Statist. 35 (3) 1105 - 1145, July 2007. https://doi.org/10.1214/009053607000000154

Information

Published: July 2007
First available in Project Euclid: 24 July 2007

zbMATH: 1175.60017
MathSciNet: MR2341700
Digital Object Identifier: 10.1214/009053607000000154

Subjects:
Primary: 60F05, 60F15, 62E20, 62G30

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 3 • July 2007
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