On a linearization of regression models

Lubomír Kubáček

Applications of Mathematics (1995)

  • Volume: 40, Issue: 1, page 61-78
  • ISSN: 0862-7940

Abstract

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An approximate value of a parameter in a nonlinear regression model is known in many cases. In such situation a linearization of the model is possible however it is important to recognize, whether the difference between the actual value of the parameter and the approximate value does not cause significant changes, e.g., in the bias of the estimator or in its variance, etc. Some rules suitable for a solution of this problem are given in the paper.

How to cite

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Kubáček, Lubomír. "On a linearization of regression models." Applications of Mathematics 40.1 (1995): 61-78. <http://eudml.org/doc/32904>.

@article{Kubáček1995,
abstract = {An approximate value of a parameter in a nonlinear regression model is known in many cases. In such situation a linearization of the model is possible however it is important to recognize, whether the difference between the actual value of the parameter and the approximate value does not cause significant changes, e.g., in the bias of the estimator or in its variance, etc. Some rules suitable for a solution of this problem are given in the paper.},
author = {Kubáček, Lubomír},
journal = {Applications of Mathematics},
keywords = {nonlinear regression model; linearization; parameter effect curvature; intrinsic curvature; parameter effect curvature; intrinsic curvature; linearization},
language = {eng},
number = {1},
pages = {61-78},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a linearization of regression models},
url = {http://eudml.org/doc/32904},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - On a linearization of regression models
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 1
SP - 61
EP - 78
AB - An approximate value of a parameter in a nonlinear regression model is known in many cases. In such situation a linearization of the model is possible however it is important to recognize, whether the difference between the actual value of the parameter and the approximate value does not cause significant changes, e.g., in the bias of the estimator or in its variance, etc. Some rules suitable for a solution of this problem are given in the paper.
LA - eng
KW - nonlinear regression model; linearization; parameter effect curvature; intrinsic curvature; parameter effect curvature; intrinsic curvature; linearization
UR - http://eudml.org/doc/32904
ER -

References

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  1. Relative curvature measures of nonlinearity, J. Roy. Stat. Soc. B 42 (1980), 1–25. (1980) MR0567196
  2. Statistické tabulky, Praha, Academia, 1958. (1958) MR0150924
  3. Nonlinear Statistical Models, Kluwer Academic Publishers, Dordrecht-Boston-London and Ister Science Press, Bratislava, 1993. (1993) MR1254661
  4. Confidence regions in nonlinear regression models, Appl. of Math. 37 (1992), 29–39. (1992) MR1152155
  5. Linear Statistical Inference and Its Applications (2nd Edition), J. Wiley, New York, 1973. (1973) MR0346957
  6. The Analysis of Variance (fifth printing), J. Wiley, New York-London-Sydney, 1967. (1967) MR1673563

Citations in EuDML Documents

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  1. Anna Jenčová, Linearization conditions for regression models with unknown variance parameter
  2. Anna Jenčová, A comparison of linearization and quadratization domains
  3. Lubomír Kubáček, Quadratic regression models
  4. Eva Tesaríková, Lubomír Kubáček, How to deal with regression models with a weak nonlinearity
  5. Lubomír Kubáček, Eva Tesaříková, Linearization regions for confidence ellipsoids
  6. Lubomír Kubáček, Linear versus quadratic estimators in linearized models
  7. Lubomír Kubáček, Linearized models with constraints of type I
  8. Lubomír Kubáček, Corrections of estimators in linearized models
  9. Lubomír Kubáček, Ludmila Kubáčková, Eva Tesaříková, Exponential regression

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