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Weak nonlinearity of growth curve models. (English) Zbl 1014.62062
The paper deals with a class of nonlinear growth curve models suitable for deformation measurements: Let several points characterizing the state of the investigated object (dam, bridge, gas holder, etc.) be located on it. Their positions are given by a coordinate vector which is, in general, known but is a nonlinear function of time and other unknown parameters. The positions of the coordinate vector are measured at several time points (epochs) and the differences of the coordinates are the basis for studying the behaviour of the investigated object deformations. Since utilization of nonlinear estimation could be complicated, linearization of the model is a standard procedure. However, this can lead to nonadmissible biases in estimators and their variances, and consequently to nonadequate interpretation of the deformations.
The paper gives sufficient conditions under which the model has the so called weak nonlinearity for the bias of the estimators of the coordinate vector and the parameters of the model and hence the estimators can be obtained by standard linearization of the model.
62H12 Estimation in multivariate analysis
62J02 General nonlinear regression
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