The Annals of Statistics

A New Approach to Least-Squares Estimation, with Applications

Sara Van De Geer

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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.

Article information

Source
Ann. Statist., Volume 15, Number 2 (1987), 587-602.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350362

Digital Object Identifier
doi:10.1214/aos/1176350362

Mathematical Reviews number (MathSciNet)
MR888427

Zentralblatt MATH identifier
0625.62046

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60G50: Sums of independent random variables; random walks 62J05: Linear regression

Keywords
Consistency entropy empirical measure uniform convergence

Citation

Geer, Sara Van De. A New Approach to Least-Squares Estimation, with Applications. Ann. Statist. 15 (1987), no. 2, 587--602. doi:10.1214/aos/1176350362. https://projecteuclid.org/euclid.aos/1176350362


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