Densities, spectral densities and modality

This paper considers the problem of specifying a simple approximating density function for a given data set (x1, . . ., xn). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities. Refinements are introduced that improve the local adaptivity of the procedures and the method is extended to spectral densities.