Nonparametric regression analysis of growth curves. (English) Zbl 0535.62088

Gasser, Theo; Müller, Hans-Georg; Köhler, Walter; Molinari, Luciano; Prader, Andrea

Ann. Stat. 12, 210-229 (1984).

Summary: In recent years, nonparametric curve estimates have been extensively explored in theoretical work. There has, however, been a certain lack of convincing applications, in particular involving comparisons with parametric techniques. The present investigation deals with the analysis of human height growth, where longitudinal measurements were collected for a sample of boys and a sample of girls. Evidence is presented that kernel estimates of acceleration and velocity of height, and of height itself, might offer advantages over a parametric fitting via functional models recently introduced.
For the specific problem considered, both approaches are biased, but the parametric one shows qualitative and quantitative distortion which both are not easily predictable. Data-analytic problems involved with kernel estimation concern the choice of kernels, the choice of the smoothing parameter, and also whether the smoothing parameter should be chosen uniformly for all subjects or individually.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
65D10	Numerical smoothing, curve fitting
62J99	Linear inference, regression
62G05	Nonparametric estimation

Keywords:

derivatives; analysis of human height growth; kernel estimates of acceleration; velocity of height