**
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.

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Acta Mathematica Universitatis Comenianae

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