In this paper we study the problem of testing the functional form
of a given regression model. A consistent test is proposed which is based on
the difference of the least squares variance estimator in the assumed
regression model and a nonparametric variance estimator. The corresponding test
statistic can be shown to be asymptotically normal under the null hypothesis
and under fixed alternatives with different rates of convergence corresponding
to both cases. This provides a simple asymptotic test, where the asymptotic
results can also be used for the calculation of the type II error of the
procedure at any particular point of the alternative and for the construction
of tests for precise hypotheses. Finally, the finite sample performance of the
new test is investigated in a detailed simulation study, which also contains a
comparison with the commonly used tests.
Publié le : 1999-06-14
Classification:
Variance estimation,
model checks,
least squares estimator,
limit theorems for quadratic forms,
62G10,
62G20,
62J05,
62J02
@article{1018031266,
author = {Dette, Holger},
title = {A consistent test for the functional form of a regression based
on a difference of variance estimators},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1012-1040},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031266}
}
Dette, Holger. A consistent test for the functional form of a regression based
on a difference of variance estimators. Ann. Statist., Tome 27 (1999) no. 4, pp. 1012-1040. http://gdmltest.u-ga.fr/item/1018031266/