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.
Publié le : 2007-07-14
Classification:
U-statistics,
central limit theorems,
empirical process,
kernel density estimation,
60F05,
60F15,
62E20,
62G30
@article{1185304000,
author = {Gin\'e, Evarist and Mason, David M.},
title = {On local U-statistic processes and the estimation of densities of functions of several sample variables},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 1105-1145},
language = {en},
url = {http://dml.mathdoc.fr/item/1185304000}
}
Giné, Evarist; Mason, David M. On local U-statistic processes and the estimation of densities of functions of several sample variables. Ann. Statist., Tome 35 (2007) no. 1, pp. 1105-1145. http://gdmltest.u-ga.fr/item/1185304000/