EMPIRICAL INFLUENCE FOR ROBUST SMOOTHING

A simple graphical method is presented to display the sensitivity of a scatter plot smoother (e.g. loess, kernel smoothers) to perturbations in the data. This enables the robustness of smoothers which have been designed to be robust to be examined directly in particular examples. Graphs are shown of various robust smoothers on several standard datasets, so that the robustness of the smoothers can be compared. The method is found to be useful in revealing features of the smoothers. Related graphs for displaying the sensitivity of a smoother to k > 1 outliers are also presented.