We shall study the general regression model $Y = g_0 (X) + \varepsilon$, where X and $varepsilon$ are independent. The available information about $g_0$ can be expressed by $g_0 \epsilon \mathscr{G}$ for some class $\mathscr{G}$. As an estimator of $g_0$ we choose the least squares estimator. We shall give necessary and sufficient conditions for consistency of this estimator in terms of (basically) geometric properties of $\mathscr{G}$. Our main tool will be the theory of empirical processes.
Publié le : 1996-12-14
Classification:
Consistency,
empirical process,
entropy,
Glivenko-Cantelli classes,
least squares estimation,
regression,
62G05,
62J02
@article{1032181165,
author = {van de Geer, Sara and Wegkamp, Marten},
title = {Consistency for the least squares estimator in nonparametric regression},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 2513-2523},
language = {en},
url = {http://dml.mathdoc.fr/item/1032181165}
}
van de Geer, Sara; Wegkamp, Marten. Consistency for the least squares estimator in nonparametric regression. Ann. Statist., Tome 24 (1996) no. 6, pp. 2513-2523. http://gdmltest.u-ga.fr/item/1032181165/