ESTIMATING THE ROOT OF A NONPARAMETRIC REGRESSION FUNCTION IN A ROBUST FASHION

For a nonparametric regression model y = m(x)+e with n independent observations, we analyze a robust method of finding the root of m(x) based on an M-estimation first discussed by Härdle & Gasser (1984). It is shown here that the robustness properties (minimaxity and breakdown function) of such an estimate are quite analogous to those of an M -estimator in the simple location model, but the rate of convergence is somewhat limited due to the nonparametric nature of the problem.