SiZer for Exploration of Structures in Curves

In the use of smoothing methods in data analysis, an important question is often: which observed features are "really there?", as opposed to being spurious sampling artifacts. An approach is described, based on scale space ideas that were originally developed in computer vision literature. Assessment of SIgni cant ZERo crossings of derivatives, results in the SiZer map, a graphical device for display of signi cance of features, with respect to both location and scale. Here "scale" means "level of resolution", i.e. "bandwidth"