Abstract: Assume thatare independent random vectors satisfying the non-parametric regression models
, for
, where
and
are smooth but unknown regression and variance functions respectively, and the error variable
is independent of
.
In this article we introduce a procedure to test the hypothesis of equality of theregression functions. The test is based on the comparison of two estimators of the distribution of the errors in each population. Kolmogorov-Smirnov and Cramér-von Mises type statistics are considered, and their asymptotic distributions are obtained. The proposed tests can detect local alternatives converging to the null hypothesis at the rate
. We describe a bootstrap procedure that approximates the critical values, and present the results of a simulation study in which the behavior of the tests for small and moderate sample sizes is studied. Finally, we include an application to a data set.
Key words and phrases: Bootstrap, Comparison of regression curves, Heteroscedastic regression, nonparametric regression.