THE FILTERED MODE TREE

The mode tree is a useful tool for visualizing the modal structure of a density. Locations of modes of the density are plotted as a function of the bandwidth used in the kernel estimate of the density. Because the mode tree uses a single bandwidth in the kernel estimator, it exhi bits all the drawbacks that a single bandwidth kernel estimator has, p articularly for densities with large tails or differences in the scale s of the modes. A modification is presented that uses the filtered ker nel estimator, a version of the kernel estimator using a small number of bandwidths. The two mode trees are compared on some synthetic data, and on a data set from DNA flow cytometry.