SiZer for exploration of structures in curves

In the use of smoothing methods in data analysis, an important question is which observed features are "really there," as opposed to being spurious sa mpling artifacts. An approach is described based on scale-space ideas origi nally developed in the computer vision literature. Assessment of SIgnifican t ZERo crossings of derivatives results in the SiZer map, a graphical devic e for display of significance of features with respect to both location and scale. Here "scale" means "level of resolution"; that is, "bandwidth."