ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIII, 2 (2004)
p. 207 - 216

Intristic Linearization of Nonlinear Regression by Principal Components Method
K. Hornisova

Abstract.  Most commonly nonlinear regression models have an important para\-meter-effect nonlinearity but only a small intrinsic nonlinearity. Hence it is of interest to approximate them linearly. This can be done either by retaining the original parametrization $\theta$, or by choosing a new parametrization $\beta=\beta(\theta)$. Under a prior weight density $\pi(\theta)$ we propose criterion of optimality of intrinsically linear approximation. The optimal solution is obtained by principal components method. The distance of the expectation surface of the new model from the expectation surface of the original one can be considered as a measure of intrinsic nonlinearity of the original model, which is simpler to compute than the well-known measure of Bates and Watts (1980). In the examples consequences for inference on parameters are examined.
Keywords: Nonlinear regression, linearization, prior, principal components analysis.

AMS Subject classification: 62J02; Secondary: 62F25.