TESTING THE EQUALITY OF NONPARAMETRIC REGRESSION CURVES

This paper proposes a test for the equality of nonparametric regression curves that does not depend on the choice of a smoothing number. The test statistic is a weighted empirical process easy to compute. It is powerful under alternatives that converge to the null at a rate n·I12 • The disturbance [ distributions are arbitrary and possibly unequal, and conditions on the regressors distribution are very mild. A simulation study demonstrates that the test enjoys good level and power propenies in small samples. We also study extensions to multiple regression, and testing the equality of several regression curves. Key words: Nonparametric testing; weighted empirical process; Donsker's invariance principle; Brownian motion; local alternatives