SFB 303 Discussion Paper No. A - 368

Author: Gasser, Theo, and Alois Kneip
Title: Searching for Structure in Curve Samples
Abstract: Increasingly often, data arise in form of samples of curves. Examples are physiological parameters measured over time for one or more samples of subjects, or measurements obtained longitudinally for various experimental units. In such a case it is important to know at an early stage of data analysis which features are occuring consistently in the sample(s) of curves. Such a definition is usually not easy due to substantial interindividual variation both in x- and y-axis, and due to the influence of noise. A method is proposed for defining features in a semi-automatic, nonparametric way in a sample of curves. The consistent occurence of some feature in a subinterval is extracted via the mode in a kernel estimated density of the estimated features. Features may be extrema, inflection points etc. ("structural points"). They are obtained via kernel estimators designed for estimating regression functions and their derivatives. Apart from a theoretical foundation, the usefullness method is documented by application to two interesting biomedical areas, i.e. research on growth and development and neurophysiology.
Keywords: Curves, Regression, Feature extraction, extrema, density, estimation
Creation-Date: May 1992
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