Statistica Sinica

Juan Carlos Pardo-Fernández, Ingrid Van Keilegom

and Wenceslao González-Manteiga

Abstract:Assume that are 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 the regression 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.