Discussiones Mathematicae Probability and Statistics 21(1) (2001) 21-48


Eva Tesaríková

Department of Algebra and Geometry,
Faculty of Science, Palacký University
Tomkova 40, CZ-779 00 Olomouc

Lubomír Kubácek

Department of Mathematical Analysis and Applied Mathematics,
Faculty of Science, Palacký University
Tomkova 40, CZ-779 00 Olomouc


If a nonlinear regression model is linearized in a non-sufficient small neighbourhood of the actual parameter, then all statistical inferences may be deteriorated. Some criteria how to recognize this are already developed. The aim of the paper is to demonstrate the behaviour of the program for utilization of these criteria.

Keywords: nonlinear regression model, criteria of linearization, demo program.

2000 Mathematics Subjects Classification: 62J02, 62J05.


[1] D.M. Bates and D.G. Watts, Relative curvature measure of nonlinearity (with discussion), Journal of the Royal Statistical Society, Ser. B. 42 (1), 1980, 1-25.
[2] D.M. Bates and D.G. Watts, Nonlinear Regression Analysis and Its Applications, J. Wiley, N. York, Chichester, Brisbane, Toronto, Singapure 1988.
[3] A. Jencová, A comparison of linearization and quadratization domains, Applications of Mathematics 42 (1997), 279-291.
[4] L. Kubácek, On a linearization of regression models, Applications of Mathematics 40 (1995), 61-78.
[5] L. Kubácek, Models with a low nonlinearity, Tatra Mountains Math. Publ. 7 (1996), 149-155.
[6] L. Kubácek, Quadratic regression models Math. Slovaca 46 (1996), 111-126.
[7] L. Kubácek and L. Kubácková, Regression Models with a weak Nonlinearity, Technical Reports, Department of Geodesy, University of Stuttgart (1998), 1-67.
[8] A. Pázman, Nonlinear Statistical Models, Kluwer Academic Publishers, Dordrecht-Boston-London 1993.

Received 13 September 2000