Open Access
April, 1995 Model Estimation in Nonlinear Regression Under Shape Invariance
Alois Kneip, Joachim Engel
Ann. Statist. 23(2): 551-570 (April, 1995). DOI: 10.1214/aos/1176324535


Given data from a sample of noisy curves, we consider a nonlinear parametric regression model with unknown model function. An iterative algorithm for estimating individual parameters as well as the model function is introduced under the assumption of a certain shape invariance: the individual regression curves are obtained from a common shape function by linear transformations of the axes. Our algorithm is based on least-squares methods for parameter estimation and on nonparametric kernel methods for curve estimation. Asymptotic distributions are derived for the individual parameter estimators as well as for the estimator of the shape function. An application to human growth data illustrates the method.


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Alois Kneip. Joachim Engel. "Model Estimation in Nonlinear Regression Under Shape Invariance." Ann. Statist. 23 (2) 551 - 570, April, 1995.


Published: April, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0828.62052
MathSciNet: MR1332581
Digital Object Identifier: 10.1214/aos/1176324535

Primary: 62J02
Secondary: 62G07

Keywords: human growth analysis , kernel estimators , Model selection , nonparametric smoothing , samples of curves , semiparametric methods

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 2 • April, 1995
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