Weakly nonlinear regression model with constraints I: nonlinear hypothesis

Lubomír Kubácek; Eva Tesaríková

Discussiones Mathematicae Probability and Statistics (2005)

  • Volume: 25, Issue: 1, page 115-133
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Lubomír Kubácek, and Eva Tesaríková. "Weakly nonlinear regression model with constraints I: nonlinear hypothesis." Discussiones Mathematicae Probability and Statistics 25.1 (2005): 115-133. <http://eudml.org/doc/287762>.

@article{LubomírKubácek2005,
abstract = {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.},
author = {Lubomír Kubácek, Eva Tesaríková},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {regression model with constraints; nonlinear hypothesis; linearization},
language = {eng},
number = {1},
pages = {115-133},
title = {Weakly nonlinear regression model with constraints I: nonlinear hypothesis},
url = {http://eudml.org/doc/287762},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Lubomír Kubácek
AU - Eva Tesaríková
TI - Weakly nonlinear regression model with constraints I: nonlinear hypothesis
JO - Discussiones Mathematicae Probability and Statistics
PY - 2005
VL - 25
IS - 1
SP - 115
EP - 133
AB - 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.
LA - eng
KW - regression model with constraints; nonlinear hypothesis; linearization
UR - http://eudml.org/doc/287762
ER -

References

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  1. [1] D.M. Bates and D.G. Watts, Relative curvature measures of nonlinearity, J. Roy. Statist. Soc. Ser. B 42 (1980), 1-25. Zbl0455.62028
  2. [2] L. Kubácek, L. Kubácková and J. Volaufová, Statistical Models with Linear Structures, Bratislava, Veda (Publishing House of Slovak Academy of Science) 1995. 
  3. [3] L. Kubácek and L. Kubácková, Regression models with a weak nonlinearity, Technical Report Nr 1998.1 Univerity of Stuttgart, 1998, 1-64. 
  4. [4] L. Kubácek and L. Kubácková, Statistics and Metrology (in Czech), Publishing House of Palacký University, Olomouc 2000. 
  5. [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. Zbl1046.62067
  6. [6] L. Kubácek, Linearized model with constraints I, Application of Mathematics 48 (2003), 81-95. Zbl1099.62067
  7. [7] A. Pázman, Nonlinear Statistical Models, Kluwer Academic Publisher, Dordrecht-Boston-London- and Ister Science Press, Bratislava 1988. Zbl0646.62056
  8. [8] C.R. Rao, Linear Statistical Inference and Its Application, J. Wiley, New York-London-Sydney 1965. Zbl0137.36203
  9. [9] C.R. Rao and S.K. Mitra, Generalized Inverse of Matrices and Its Applications, New York, J. Wiley 1971. Zbl0236.15004
  10. [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. Zbl1060.62067

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