The Annals of Statistics

Estimating a Regression Function

Sara van de Geer

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Abstract

In this paper, an entropy approach is proposed to establish rates of convergence for estimators of a regression function. General regression problems are considered, with linear regression, splines and isotonic regression as special cases. The estimation methods studied are least squares, least absolute deviations and penalized least squares. Common features of these methods and various regression problems are highlighted.

Article information

Source
Ann. Statist., Volume 18, Number 2 (1990), 907-924.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347632

Digital Object Identifier
doi:10.1214/aos/1176347632

Mathematical Reviews number (MathSciNet)
MR1056343

Zentralblatt MATH identifier
0709.62040

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60G50: Sums of independent random variables; random walks 62J99: None of the above, but in this section

Keywords
Empirical processes entropy least absolute deviations (penalized) least squares rates of convergence

Citation

van de Geer, Sara. Estimating a Regression Function. Ann. Statist. 18 (1990), no. 2, 907--924. doi:10.1214/aos/1176347632. https://projecteuclid.org/euclid.aos/1176347632


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