Searching for structure in curve samples

The shape of a regression curve can to a large extent be characterized by the succession of structural features like extrema, inflection points, and so on. When analyzing a sample of regression curves, it is often important to know al an early stage of data analysis which structural features are occurring consistently in each curve of the sample. Such a definition is usually nor easy due to substantial interindividual variation both in the x and the y axis and due to the influence of noise. A method is proposed for identifying typical features without relying on an a priori specified functional model for the curves. The approach is based on the frequencies of occurrence of structural features, as, for example, maxima in the curve sample along the x axis. Important tools are nonparametric regression and differentiation and kernel density estimation. Apart from a theoretical foundation, the usefulness of the method is documented by application to two interesting biomedical areas: growth and development, and neurophysiology.