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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

Abstract

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.

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

Information

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

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

Subjects:
Primary: 62G05
Secondary: 62J02

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 6 • December 1996
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