Strong uniform consistency rates are established for kernel type estimators of functionals of the conditional distribution function, under general conditions. The present treatment unifies a number of specific problems previously studied separately in the literature. Some of these applications we treat in detail, including regression curve estimation, density estimation, estimation of conditional df's, $L$-smoothing and $M$-smoothing. Various previous results in the literature are extended and/or sharpened.
Publié le : 1988-12-14
Classification:
Strong uniform consistency rates,
nonparametric kernel estimators,
density estimation,
$L$-smoother,
$M$-smoother,
regression function estimation,
62G05,
60F15
@article{1176351047,
author = {Hardle, W. and Janssen, P. and Serfling, R.},
title = {Strong Uniform Consistency Rates for Estimators of Conditional Functionals},
journal = {Ann. Statist.},
volume = {16},
number = {1},
year = {1988},
pages = { 1428-1449},
language = {en},
url = {http://dml.mathdoc.fr/item/1176351047}
}
Hardle, W.; Janssen, P.; Serfling, R. Strong Uniform Consistency Rates for Estimators of Conditional Functionals. Ann. Statist., Tome 16 (1988) no. 1, pp. 1428-1449. http://gdmltest.u-ga.fr/item/1176351047/