ROBUST NONPARAMETRIC FUNCTION ESTIMATION

The bias of kernel methods based on local constant fits can have an ad verse effect when the derivative of the marginal density or that of th e regression function is large. The drawback can be repaired by consid ering a class of kernel estimators based on local linear fits. These e stimators have the desired asymptotic properties and can be used to es timate conditional quantiles and to robustify the usual mean regressio n. The conditional asymptotic normality of these estimators at both bo undary and interior points is established. An important consequence of the study is that the proposed method has the desired sampling proper ties at both boundary and interior points of the support of the design density. Therefore, our procedure does not require boundary modificat ions. Applications of such a local linear approximation method are dis cussed.