Comparison of non-parametric regression functions through their cumulatives

In this work we present a simple estimator for the cumulative regression function that involves no smoothing and we give its asymptotic distribution. By comparing cumulatives a test for comparison of nonparametric regression functions is proposed. The proposed test does not involve a smoothing parameter and has good power against alternatives that are uniformly ordered. The test-statistic works for both fixed and random designs. (C) 2000 Elsevier Science B.V. All rights reserved.