A new test is proposed for the comparison of two regression curves
$f$ and $g$. We prove an asymptotic normal law under fixed
alternatives which can be applied for power calculations, for constructing
confidence regions and for testing precise hypotheses of a weighted $L_2$
distance between $f$ and $g$ . In particular, the problem of nonequal
sample sizes is treated, which is related to a peculiar formula of the area
between two step functions. These results are extended in various directions,
such as the comparison of $k$ regression functions or the optimal
allocation of the sample sizes when the total sample size is fixed. The
proposed pivot statistic is not based on a nonparametric estimator of the
regression curves and therefore does not require the specification of any
smoothing parameter.
Publié le : 1998-12-14
Classification:
Comparison of regression curves,
nonparametric analysis of covariance,
heteroscedastic errors,
$k$-sample problem,
62G05,
62G10,
62G30,
62G07
@article{1024691474,
author = {Munk, Axel and Dette, Holger},
title = {Nonparametric comparison of several regression functions: exact
and asymptotic theory},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 2339-2368},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691474}
}
Munk, Axel; Dette, Holger. Nonparametric comparison of several regression functions: exact
and asymptotic theory. Ann. Statist., Tome 26 (1998) no. 3, pp. 2339-2368. http://gdmltest.u-ga.fr/item/1024691474/