How to deal with regression models with a weak nonlinearity

Eva Tesaríková; Lubomír Kubáček

Discussiones Mathematicae Probability and Statistics (2001)

  • Volume: 21, Issue: 1, page 21-48
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Eva Tesaríková, and Lubomír Kubáček. "How to deal with regression models with a weak nonlinearity." Discussiones Mathematicae Probability and Statistics 21.1 (2001): 21-48. <http://eudml.org/doc/287641>.

@article{EvaTesaríková2001,
abstract = {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.},
author = {Eva Tesaríková, Lubomír Kubáček},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {nonlinear regression model; criteria of linearization; demo program},
language = {eng},
number = {1},
pages = {21-48},
title = {How to deal with regression models with a weak nonlinearity},
url = {http://eudml.org/doc/287641},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Eva Tesaríková
AU - Lubomír Kubáček
TI - How to deal with regression models with a weak nonlinearity
JO - Discussiones Mathematicae Probability and Statistics
PY - 2001
VL - 21
IS - 1
SP - 21
EP - 48
AB - 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.
LA - eng
KW - nonlinear regression model; criteria of linearization; demo program
UR - http://eudml.org/doc/287641
ER -

References

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  1. [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. Zbl0455.62028
  2. [2] D.M. Bates and D.G. Watts, Nonlinear Regression Analysis and Its Applications, J. Wiley, N. York, Chichester, Brisbane, Toronto, Singapure 1988. Zbl0728.62062
  3. [3] A. Jencová, A comparison of linearization and quadratization domains, Applications of Mathematics 42 (1997), 279-291. Zbl0898.62084
  4. [4] L. Kubáček, On a linearization of regression models, Applications of Mathematics 40 (1995), 61-78. Zbl0819.62054
  5. [5] L. Kubáček, Models with a low nonlinearity, Tatra Mountains Math. Publ. 7 (1996), 149-155. Zbl0925.62254
  6. [6] L. Kubáček, Quadratic regression models Math. Slovaca 46 (1996), 111-126. Zbl0848.62033
  7. [7] L. Kubáček and L. Kubácková, Regression Models with a weak Nonlinearity, Technical Reports, Department of Geodesy, University of Stuttgart (1998), 1-67. 
  8. [8] A. Pázman, Nonlinear Statistical Models, Kluwer Academic Publishers, Dordrecht-Boston-London 1993. 

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