We investigate the almost sure convergence of a kernel-type conditional empirical distribution function both in sup-norm and weighted sup-norms. As an application we get a strong law for the Nadaraya-Watson estimate of a regression function $m(\mathbf{x}) = \mathbb{E}(Y\mid \mathbf{X} = \mathbf{x})$ under a weak moment condition on $Y$.
Publié le : 1986-07-14
Classification:
Conditional empirical distribution function,
Glivenko-Cantelli convergence,
weight functions,
Nadaraya-Watson estimator,
60F15,
62G05,
62J02
@article{1176992445,
author = {Stute, Winfried},
title = {On Almost Sure Convergence of Conditional Empirical Distribution Functions},
journal = {Ann. Probab.},
volume = {14},
number = {4},
year = {1986},
pages = { 891-901},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992445}
}
Stute, Winfried. On Almost Sure Convergence of Conditional Empirical Distribution Functions. Ann. Probab., Tome 14 (1986) no. 4, pp. 891-901. http://gdmltest.u-ga.fr/item/1176992445/