The Annals of Statistics

Weak convergence of the empirical process of residuals in linear models with many parameters

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.

Article information

Source
Ann. Statist., Volume 29, Issue 3 (2001), 748-762.

Dates
First available in Project Euclid: 24 December 2001

Permanent link to this document
https://projecteuclid.org/euclid.aos/1009210688

Digital Object Identifier
doi:10.1214/aos/1009210688

Mathematical Reviews number (MathSciNet)
MR1865339

Zentralblatt MATH identifier
1012.62016

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62J99: None of the above, but in this section

Citation

Chen, Gemai; and Lockhart, Richard A. Weak convergence of the empirical process of residuals in linear models with many parameters. Ann. Statist. 29 (2001), no. 3, 748--762. doi:10.1214/aos/1009210688. https://projecteuclid.org/euclid.aos/1009210688

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