In the context of regression analysis it is known that the residual
cusum process may serve as a basis for the construction of various omnibus,
smooth and directional goodness-of-fit tests. Since a deeper analysis requires
the decomposition of the cusums into their principal components and this is
difficult to obtain, we propose to replace this process by its innovation
martingale. It turns out that the resulting tests are (asymptotically)
distribution free under composite null models and may be readily performed. A
simulation study is included which indicates that the distributional
approximations already work for small to moderate sample sizes.
@article{1024691363,
author = {Stute, Winfried and Thies, Silke and Zhu, Li-Xing},
title = {Model checks for regression: an innovation process
approach},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 1916-1934},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691363}
}
Stute, Winfried; Thies, Silke; Zhu, Li-Xing. Model checks for regression: an innovation process
approach. Ann. Statist., Tome 26 (1998) no. 3, pp. 1916-1934. http://gdmltest.u-ga.fr/item/1024691363/