Open Access
December 1996 Consistency for the least squares estimator in nonparametric regression
Marten Wegkamp, Sara van de Geer
Ann. Statist. 24(6): 2513-2523 (December 1996). DOI: 10.1214/aos/1032181165


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.


Download Citation

Marten Wegkamp. Sara van de Geer. "Consistency for the least squares estimator in nonparametric regression." Ann. Statist. 24 (6) 2513 - 2523, December 1996.


Published: December 1996
First available in Project Euclid: 16 September 2002

zbMATH: 0867.62027
MathSciNet: MR1425964
Digital Object Identifier: 10.1214/aos/1032181165

Primary: 62G05
Secondary: 62J02

Keywords: consistency , empirical process , Entropy , Glivenko-Cantelli classes , Least squares estimation , regression

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 6 • December 1996
Back to Top