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June 2001 Weak convergence of the empirical process of residuals in linear models with many parameters
Gemai and Chen, Richard A. Lockhart
Ann. Statist. 29(3): 748-762 (June 2001). DOI: 10.1214/aos/1009210688

Abstract

When fitting, by least squares, a linear model (with an intercept term) with $p$ parameters to $n$ data points, the asymptotic behavior of the residual empirical process is shown to be the same as in the single sample problem provided $p^3 \log^2 (p) /n \to 0$ for any error density having finite variance and a bounded first derivative. No further conditions are imposed on the sequence of design matrices. The result is extended to more general estimates with the property that the average error and average squared error in the fitted values are on the same order as for least squares.

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Gemai and Chen. Richard A. Lockhart. "Weak convergence of the empirical process of residuals in linear models with many parameters." Ann. Statist. 29 (3) 748 - 762, June 2001. https://doi.org/10.1214/aos/1009210688

Information

Published: June 2001
First available in Project Euclid: 24 December 2001

MathSciNet: MR1865339
zbMATH: 1012.62016
Digital Object Identifier: 10.1214/aos/1009210688

Subjects:
Primary: 62E20
Secondary: 62J99

Keywords: Empirical processes , Goodness-of-fit , regression , residual

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 3 • June 2001
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