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{1009210688,
author = {Chen, Gemai and and Lockhart, Richard A.},
title = {Weak convergence of the empirical process of residuals in linear
models with many parameters},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 748-762},
language = {en},
url = {http://dml.mathdoc.fr/item/1009210688}
}
Chen, Gemai and; Lockhart, Richard A. Weak convergence of the empirical process of residuals in linear
models with many parameters. Ann. Statist., Tome 29 (2001) no. 2, pp. 748-762. http://gdmltest.u-ga.fr/item/1009210688/