The problem considered is under which conditions in weakly nonlinear regression model with constraints I a weakly nonlinear hypothesis can be tested by linear methods. The aim of the paper is to find a region around the approximate value of the regression parameter with the following property. If we are certain that the actual value of the regression parameter is in this region, then the linear method of testing can be used without any significant deterioration of the inference.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1065,
author = {Lubom\'\i r Kub\'acek and Eva Tesar\'\i kov\'a},
title = {Weakly nonlinear regression model with constraints I: nonlinear hypothesis},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {25},
year = {2005},
pages = {115-133},
zbl = {1102.62069},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1065}
}
Lubomír Kubácek; Eva Tesaríková. Weakly nonlinear regression model with constraints I: nonlinear hypothesis. Discussiones Mathematicae Probability and Statistics, Tome 25 (2005) pp. 115-133. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1065/
[000] [1] D.M. Bates and D.G. Watts, Relative curvature measures of nonlinearity, J. Roy. Statist. Soc. Ser. B 42 (1980), 1-25. | Zbl 0455.62028
[001] [2] L. Kubácek, L. Kubácková and J. Volaufová, Statistical Models with Linear Structures, Bratislava, Veda (Publishing House of Slovak Academy of Science) 1995.
[002] [3] L. Kubácek and L. Kubácková, Regression models with a weak nonlinearity, Technical Report Nr 1998.1 Univerity of Stuttgart, 1998, 1-64.
[003] [4] L. Kubácek and L. Kubácková, Statistics and Metrology (in Czech), Publishing House of Palacký University, Olomouc 2000.
[004] [5] L. Kubácek and L. Kubácková, Statistical problems of a determination of isobestic points, Folia Fa. Sci. Nat. Univ. Masarykianae Brunensis, Mathematica 11 (2002), 139-150. | Zbl 1046.62067
[005] [6] L. Kubácek, Linearized model with constraints I, Application of Mathematics 48 (2003), 81-95. | Zbl 1099.62067
[006] [7] A. Pázman, Nonlinear Statistical Models, Kluwer Academic Publisher, Dordrecht-Boston-London- and Ister Science Press, Bratislava 1988. | Zbl 0646.62056
[007] [8] C.R. Rao, Linear Statistical Inference and Its Application, J. Wiley, New York-London-Sydney 1965. | Zbl 0137.36203
[008] [9] C.R. Rao and S.K. Mitra, Generalized Inverse of Matrices and Its Applications, New York, J. Wiley 1971. | Zbl 0236.15004
[009] [10] E. Tesaríková and L. Kubácek, A test in nonlinear regression models, (in Czech), Demoprogram, Department of Algebra and Geometry, Faculty of Science, Palacký University, Olomouc 2004. | Zbl 1060.62067