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June, 1987 A New Approach to Least-Squares Estimation, with Applications
Sara Van De Geer
Ann. Statist. 15(2): 587-602 (June, 1987). DOI: 10.1214/aos/1176350362

Abstract

The regression model $\mathbf{y} = g(\mathbf{x}) + \mathbf{\varepsilon}$ and least-squares estimation are studied in a general context. By making use of empirical process theory, it is shown that entropy conditions on the class $\mathscr{G}$ of possible regression functions imply $L^2$-consistency of the least-squares estimator $\hat{\mathbf{g}}_n$ of $g$. This result is applied in parametric and nonparametric regression.

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Sara Van De Geer. "A New Approach to Least-Squares Estimation, with Applications." Ann. Statist. 15 (2) 587 - 602, June, 1987. https://doi.org/10.1214/aos/1176350362

Information

Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0625.62046
MathSciNet: MR888427
Digital Object Identifier: 10.1214/aos/1176350362

Subjects:
Primary: 60B10
Secondary: 60G50, 62J05

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 2 • June, 1987
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