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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1018, author = {Eva Tesar\'\i kov\'a and Lubom\'\i r Kub\'a\v cek}, title = {How to deal with regression models with a weak nonlinearity}, journal = {Discussiones Mathematicae Probability and Statistics}, volume = {21}, year = {2001}, pages = {21-48}, zbl = {0984.62044}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1018} }
Eva Tesaríková; Lubomír Kubáček. How to deal with regression models with a weak nonlinearity. Discussiones Mathematicae Probability and Statistics, Tome 21 (2001) pp. 21-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1018/
[000] [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. | Zbl 0455.62028
[001] [2] D.M. Bates and D.G. Watts, Nonlinear Regression Analysis and Its Applications, J. Wiley, N. York, Chichester, Brisbane, Toronto, Singapure 1988. | Zbl 0728.62062
[002] [3] A. Jencová, A comparison of linearization and quadratization domains, Applications of Mathematics 42 (1997), 279-291. | Zbl 0898.62084
[003] [4] L. Kubáček, On a linearization of regression models, Applications of Mathematics 40 (1995), 61-78. | Zbl 0819.62054
[004] [5] L. Kubáček, Models with a low nonlinearity, Tatra Mountains Math. Publ. 7 (1996), 149-155. | Zbl 0925.62254
[005] [6] L. Kubáček, Quadratic regression models Math. Slovaca 46 (1996), 111-126. | Zbl 0848.62033
[006] [7] L. Kubáček and L. Kubácková, Regression Models with a weak Nonlinearity, Technical Reports, Department of Geodesy, University of Stuttgart (1998), 1-67.
[007] [8] A. Pázman, Nonlinear Statistical Models, Kluwer Academic Publishers, Dordrecht-Boston-London 1993.