Linearized regression model with constraints of type II

Lubomír Kubáček

Applications of Mathematics (2003)

  • Volume: 48, Issue: 3, page 175-191
  • ISSN: 0862-7940

Abstract

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A linearization of the nonlinear regression model causes a bias in estimators of model parameters. It can be eliminated, e.g., either by a proper choice of the point where the model is developed into the Taylor series or by quadratic corrections of linear estimators. The aim of the paper is to obtain formulae for biases and variances of estimators in linearized models and also for corrected estimators.

How to cite

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Kubáček, Lubomír. "Linearized regression model with constraints of type II." Applications of Mathematics 48.3 (2003): 175-191. <http://eudml.org/doc/33143>.

@article{Kubáček2003,
abstract = {A linearization of the nonlinear regression model causes a bias in estimators of model parameters. It can be eliminated, e.g., either by a proper choice of the point where the model is developed into the Taylor series or by quadratic corrections of linear estimators. The aim of the paper is to obtain formulae for biases and variances of estimators in linearized models and also for corrected estimators.},
author = {Kubáček, Lubomír},
journal = {Applications of Mathematics},
keywords = {nonlinear regression model; linearization; constraints of type II; nonlinear regression model; linearization; constraints of type II},
language = {eng},
number = {3},
pages = {175-191},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linearized regression model with constraints of type II},
url = {http://eudml.org/doc/33143},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - Linearized regression model with constraints of type II
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 3
SP - 175
EP - 191
AB - A linearization of the nonlinear regression model causes a bias in estimators of model parameters. It can be eliminated, e.g., either by a proper choice of the point where the model is developed into the Taylor series or by quadratic corrections of linear estimators. The aim of the paper is to obtain formulae for biases and variances of estimators in linearized models and also for corrected estimators.
LA - eng
KW - nonlinear regression model; linearization; constraints of type II; nonlinear regression model; linearization; constraints of type II
UR - http://eudml.org/doc/33143
ER -

References

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  1. Relative curvature measures of nonlinearity, J.  Roy. Statist. Soc. B42 (1980), 1–25. (1980) MR0567196
  2. Statistical Models with Linear Structures, Veda, Bratislava, 1995. (1995) 
  3. One of the calibration problems, Acta Univ. Palack. Olomuc., Mathematica 36 (1997), 117–130. (1997) MR1620541
  4. Regression models with a weak nonlinearity, Technical Report Nr. 1998.1, Universität Stuttgart, 1998, pp. 1–67. (1998) 
  5. Statistics and Metrology, Palacký University in Olomouc–Publishing House, 2000. (Czech) (2000) 
  6. Unified theory of linear estimation, Sankhya A 33 (1971), 371–394. (1971) Zbl0236.62048MR0319321
  7. Generalized Inverse of Matrices and Its Applications, J.  Wiley, N.  York-London-Sydney-Toronto, 1971. (1971) Zbl0236.15005MR0338013

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