In the problem of testing the equalityof k regression
curves from independent samples, we discuss three methods using nonparametric
estimators of the regression function. The first test is based on a linear
combination of estimators for the integrated variance function in the
individual samples and in the combined sample. The second approach transfers
the classical one-way analysis of variance to the situation of comparing
non-parametric curves, while the third test compares the differences between
the estimates of the individual regression functions by means of an
$L^2$-distance.We prove asymptotic normality of all considered statistics under
the null hypothesis and local and fixed alternatives with different rates
corresponding to the various cases. Additionally,consistency of a wild
bootstrap version of the tests is established. In contrast to most of the
procedures proposed in the literature, the methods introduced in this paper are
also applicable in the case of different design points in each sample and
heteroscedastic errors. A simulation studyis conducted to investigate the
finite sample properties of the new tests and a comparison with recently
proposed and related procedures is performed.