The Annals of Statistics

Nonparametric Regression Analysis of Growth Curves

Theo Gasser, Hans-Georg Muller, Walter Kohler, Luciano Molinari, and Andrea Prader

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Abstract

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.

Article information

Source
Ann. Statist., Volume 12, Number 1 (1984), 210-229.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346402

Digital Object Identifier
doi:10.1214/aos/1176346402

Mathematical Reviews number (MathSciNet)
MR733509

Zentralblatt MATH identifier
0535.62088

JSTOR
links.jstor.org

Subjects
Primary: 65D10: Smoothing, curve fitting
Secondary: 62D25 62J99: None of the above, but in this section 62G05: Estimation 92A05

Keywords
Kernel estimates growth curves derivatives nonparametric regression

Citation

Gasser, Theo; Muller, Hans-Georg; Kohler, Walter; Molinari, Luciano; Prader, Andrea. Nonparametric Regression Analysis of Growth Curves. Ann. Statist. 12 (1984), no. 1, 210--229. doi:10.1214/aos/1176346402. https://projecteuclid.org/euclid.aos/1176346402


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Corrections

  • See Correction: Theo Gasser, Hans-Georg Muller, Walter Kohler, Luciano Molinari, Andrea Prader. Correction: Nonparametric Regression Analysis of Growth Curves. Ann. Statist., Volume 12, Number 4 (1984), 1588--1588.