Let a linear regression be given. For detecting change-points, it is
usual to consider the sequence of partial sums of least squares residuals
whence a partial sums process is defined. Given a sequence of exact
experimental designs, we consider for each design the corresponding partial
sums process. If the sequence of designs converges to a continuous design, we
derive the explicit form of the limit process of the corresponding sequence of
partial sums processes. This is a complicated function of the Brownian motion.
These results are useful for the problem of testing for change of regression at
known or unknown times.
Publié le : 1998-08-14
Classification:
Linear regression,
regression residuals,
partial sums process,
functional central limit theorem,
functions of Brownian motion,
change-point problems,
tests,
60F17,
60G15,
62J05
@article{1024691248,
author = {Bischoff, Wolfgang},
title = {A functional central limit theorem for regression models},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 1398-1410},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691248}
}
Bischoff, Wolfgang. A functional central limit theorem for regression models. Ann. Statist., Tome 26 (1998) no. 3, pp. 1398-1410. http://gdmltest.u-ga.fr/item/1024691248/