Searching for structure in curve samples

• 成果类型: Article
• 署名作者: Gasser, T; Kneip, A
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2291510
• 发表日期: 1995
• 页码: 1179-1188
• 关键词: kernel regression; Nonparametric Regression; bandwidth choice; mid-growth; height; estimators; CHILDREN; variance; errors; spurt

摘要

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.